Alg2 Graphing Rational Functions (One More)
•Download as PPTX, PDF•
2 likes•383 views
This document provides a step-by-step example of graphing a rational function. It outlines the key steps as factoring the function, simplifying it to find any vertical asymptotes or holes, determining the horizontal asymptote by comparing the highest degree terms and coefficients, and creating a table of x and y values to find more points to graph the function. The example rational function has a vertical asymptote at x = -3 and a hole at the point (2,1).
Report
Share
Report
Share
Recommended
Solving Quadratics
The document discusses three forms of quadratic equations - standard form, vertex form, and intercept form. It provides the definitions and formulas for each form. It then explains how to graph each form by identifying key features of the equation, finding important points like the vertex, axis of symmetry, intercepts, and connecting points to sketch the parabolic curve. Graphing techniques include using the value of a to determine the opening direction, using b and c for standard form, using h and k for vertex form, and using p and q for intercepts form.
PreAlgebra 1.8
The document describes key concepts about the coordinate plane, including that it is formed by the intersection of the x-axis and y-axis at the origin point, dividing it into four quadrants. Points on the coordinate plane are represented by ordered pairs using their x-coordinate and y-coordinate. Examples are given of plotting points from their coordinates and reading point locations. A scatter plot on a coordinate plane can show relationships between paired data by plotting each data pair as a point.
Interesting Mathematics3- Belgium
The surface of a triangle through three points A(x1,y1), B(x2,y2), and C(x3,y3) can be found by calculating the absolute value of the determinant of the matrix with the x- and y-coordinates of the three points. For example, the surface of the triangle through points A(-3,-3), B(5,1), and C(-1,-3) is 4, as calculated from the determinant of the matrix with their coordinates.
Basic Analytical Geometry
This document provides an overview of analytic geometry in 3 paragraphs or less. It introduces analytic geometry as a branch of mathematics that uses algebraic equations to describe geometric figures on a coordinate system. It was developed in the 1630s by Descartes and Fermat and allowed geometry and algebra to be linked by describing geometric concepts like points and lines with real numbers and equations. The key concept is using a coordinate system to assign unique real number coordinates to each point, allowing geometric shapes to be represented by algebraic equations.
Msm1 fl ch11_03
The document provides information about coordinate planes and ordered pairs:
- A coordinate plane is formed by two number lines (x-axis and y-axis) intersecting at right angles at the origin point (0,0).
- Ordered pairs (x,y) are used to identify points in the coordinate plane, with x being the distance from the y-axis and y being the distance from the x-axis.
- Examples are given of naming quadrants, writing coordinates of points, and graphing points on a coordinate plane.
Coordinate plane
The document introduces the coordinate plane as a tool for working with equations in two variables. It explains how to create a coordinate plane by drawing perpendicular x and y axes that intersect at the origin, and using the axes to locate points on the plane using ordered pairs of numbers (x,y) as coordinates. It describes how to plot points by starting at the origin and counting along the x-axis and y-axis according to the x and y coordinates of the point. Finally, it divides the coordinate plane into four quadrants.
Hoag Ordered Pairs Lesson
Students will be able to identify the parts of a coordinate grid and correctly graph an ordered pair on a grid.
5 1c Graphing lines from a point and slope
Given a point and slope, this document provides instructions for graphing the line through that point with the given slope. It explains that you should plot the point, determine if the slope is positive, negative, zero, or undefined, then use the slope to move up/down and over from the point to draw the line. It also notes that if the slope is a whole number, it should be converted to a ratio, and provides examples of graphing lines from different points with various slopes.
Recommended
Solving Quadratics
The document discusses three forms of quadratic equations - standard form, vertex form, and intercept form. It provides the definitions and formulas for each form. It then explains how to graph each form by identifying key features of the equation, finding important points like the vertex, axis of symmetry, intercepts, and connecting points to sketch the parabolic curve. Graphing techniques include using the value of a to determine the opening direction, using b and c for standard form, using h and k for vertex form, and using p and q for intercepts form.
PreAlgebra 1.8
The document describes key concepts about the coordinate plane, including that it is formed by the intersection of the x-axis and y-axis at the origin point, dividing it into four quadrants. Points on the coordinate plane are represented by ordered pairs using their x-coordinate and y-coordinate. Examples are given of plotting points from their coordinates and reading point locations. A scatter plot on a coordinate plane can show relationships between paired data by plotting each data pair as a point.
Interesting Mathematics3- Belgium
The surface of a triangle through three points A(x1,y1), B(x2,y2), and C(x3,y3) can be found by calculating the absolute value of the determinant of the matrix with the x- and y-coordinates of the three points. For example, the surface of the triangle through points A(-3,-3), B(5,1), and C(-1,-3) is 4, as calculated from the determinant of the matrix with their coordinates.
Basic Analytical Geometry
This document provides an overview of analytic geometry in 3 paragraphs or less. It introduces analytic geometry as a branch of mathematics that uses algebraic equations to describe geometric figures on a coordinate system. It was developed in the 1630s by Descartes and Fermat and allowed geometry and algebra to be linked by describing geometric concepts like points and lines with real numbers and equations. The key concept is using a coordinate system to assign unique real number coordinates to each point, allowing geometric shapes to be represented by algebraic equations.
Msm1 fl ch11_03
The document provides information about coordinate planes and ordered pairs:
- A coordinate plane is formed by two number lines (x-axis and y-axis) intersecting at right angles at the origin point (0,0).
- Ordered pairs (x,y) are used to identify points in the coordinate plane, with x being the distance from the y-axis and y being the distance from the x-axis.
- Examples are given of naming quadrants, writing coordinates of points, and graphing points on a coordinate plane.
Coordinate plane
The document introduces the coordinate plane as a tool for working with equations in two variables. It explains how to create a coordinate plane by drawing perpendicular x and y axes that intersect at the origin, and using the axes to locate points on the plane using ordered pairs of numbers (x,y) as coordinates. It describes how to plot points by starting at the origin and counting along the x-axis and y-axis according to the x and y coordinates of the point. Finally, it divides the coordinate plane into four quadrants.
Hoag Ordered Pairs Lesson
Students will be able to identify the parts of a coordinate grid and correctly graph an ordered pair on a grid.
5 1c Graphing lines from a point and slope
Given a point and slope, this document provides instructions for graphing the line through that point with the given slope. It explains that you should plot the point, determine if the slope is positive, negative, zero, or undefined, then use the slope to move up/down and over from the point to draw the line. It also notes that if the slope is a whole number, it should be converted to a ratio, and provides examples of graphing lines from different points with various slopes.
Coordinate Plane[1]
The coordinate plane is formed by two perpendicular number lines intersecting at their zero points. It is divided into four quadrants by the x-axis and y-axis. An ordered pair (x, y) assigns a point's location by its x and y coordinates. To plot a point, start at the origin and locate the x value on the x-axis, then move up or down to the y value.
6th Math (C2) - Lesson 41--Dec15
This document contains instructions for assignment set 41 that is due tomorrow. It reviews the distributive property of multiplication over addition using examples like 3(2 + 5) and provides 5 practice problems: A) finding the area of a rectangle, B) evaluating a multiplication expression, C) simplifying 6(20 - 5) in 2 ways, D) simplifying 2(n + 5), and E) writing 2 formulas for finding the perimeter of a rectangle.
Ch6.3 Point-Slope Form
This document discusses point-slope form for writing the equation of a line given a point and slope. It provides examples of writing equations of lines using point-slope form, including lines with a given slope that pass through a point, lines that pass through two given points, lines parallel or perpendicular to another line that pass through a given point, and converting an equation in point-slope form to slope-intercept form. Exercises are provided from page 256 problems 3 through 20.
Mth 518 report grapes_garachico
GRAPES is software that allows users to draw and manipulate graphs of functions, relations, curves, and other mathematical objects. It has tools for inputting and editing functions and relations, operating on graphs by changing parameters or dragging points, and analyzing functions through tools like the function value window or definite integral window. The document provides examples of using GRAPES to draw and explore properties of linear and quadratic equations, converting between slope-intercept form and general form for lines, and using the quadratic formula to solve quadratic equations.
5.4 Slope Intercept Form
The document provides an overview of slope-intercept form for linear equations. It defines slope as the constant rate of change and the y-intercept as the y-value when x=0. Slope-intercept form is given as y=mx+b, where m is the slope and b is the y-intercept. This form can be used to graph lines, find points, and describe situations with a constant rate of change. Understanding slope-intercept form is important for showing what y-values occur at different x-values for a linear relationship.
anova Statistical analysis
1) The document discusses various statistical analysis techniques including data tabulation, graphical representation, standard deviation, ANOVA, and linear regression analysis.
2) Data tabulation involves arranging data in logical tables to reduce space, explanations, and help with comparisons. Graphical representation involves using charts like linear, bar, and pie charts to visually depict relationships.
3) Standard deviation and standard error are discussed as measures of dispersion in a data series and sampling distribution respectively. ANOVA and linear regression are analyzed as methods to understand relationships between variables and predict outcomes.
2.5 Equations of Lines
This document discusses equations of lines, including linear functions and their standard, point-slope, and slope-intercept forms. It defines parallel and perpendicular lines based on their slopes. It provides examples of writing the equation of a line from its graph or from a point and slope. Key steps include calculating the slope, selecting a point, and writing the equation in the appropriate form.
Coordinate Plane
The document defines and explains the key elements of the coordinate plane, including the x and y axes which intersect at the origin (0,0) to form four quadrants. Points on the plane are represented by coordinates (x,y) and are plotted by starting at the origin and moving right along the x-axis and up/down along the y-axis. The quadrants are numbered I through IV based on whether the x and y values are positive or negative.
Coordinate Plane Review
The document discusses key concepts about the coordinate plane, including:
1) Plotting points on the coordinate plane using ordered pairs like (1,1) and identifying which quadrant points fall into.
2) The coordinate plane is divided into four quadrants based on whether the x and y values are positive or negative.
3) Transformations like translations can change the position of shapes on the coordinate plane by sliding or shifting them along the x- or y-axis.
Md university cmis 102 week 3 hands
cmis 102 homework 3 new,cmis 102 week 3 hands on lab new,md university cmis 102,cmis 102,md university cmis 102 week 3 tutorial,cmis 102 week 3 assignment,md university cmis 102 week 3 help
Coordinate plane
The document discusses graphing ordered pairs on a coordinate plane. It defines key terms like coordinate, plane, axes, quadrants, and ordered pairs. It explains that the x-axis is horizontal, the y-axis is vertical, and they intersect at the origin (0,0). Ordered pairs use the format (x,y) to locate points by giving the x-coordinate first and y-coordinate second. Several examples are given to demonstrate graphing points in the quadrants of the coordinate plane.
Math presentation2551
The document provides steps to find lines parallel and perpendicular to the given line 2x - 3y = 9 through the point (4, -1). It is given that the slope of the original line is 2/3. The parallel line has the same slope of 2/3, while the perpendicular line has the slope of the negative reciprocal -3/2. Equations for both the parallel and perpendicular lines through the given point are provided.
Intro to coordinate plane
Into to the Coordiante Plane Lesson-Fred Jones-Teach to the eyes example.
Mathematics
Goes to the Holt Course 2 Book.
Algebra booklet
This document provides an introduction to algebra and quadratic expressions and equations, including definitions of key terms like variables, coefficients, and algebraic expressions. It covers topics like expanding, simplifying, and factorizing quadratic expressions using various methods. Real-world applications of quadratic equations are discussed, such as their use in physics, finance, and everyday contexts involving areas, profits, speeds, lenses, and mirrors.
Cartesian coordinate plane
The document discusses the Cartesian coordinate plane and functions. It defines the Cartesian plane as being formed by two perpendicular number lines called the x-axis and y-axis that intersect at the origin (0,0). It describes how each point on the plane is associated with an ordered pair (x,y) denoting its coordinates and how the plane is divided into four quadrants. It then demonstrates how to plot various points on the plane by starting at the origin and moving right or left along the x-axis and up or down along the y-axis. Finally, it discusses relations and functions, defining a function as a relation where each x-value is mapped to only one y-value.
Applied Calculus: An introduction about Real Numbers and Real Line
Lecture #: 01: "An introduction about Real Numbers & Real Line" with in a course on Applied Calculus offered at Faculty of Engineering, University of Central Punjab
By: Prof. Muhammad Rafiq.
Ap Physics C Mathematical Concepts Vectors
This document covers mathematical concepts related to AP Physics C including:
1) Polynomials of different orders and their graphs.
2) Trigonometry definitions and relationships using right triangles.
3) Vectors having both direction and magnitude, while scalars have only magnitude. Vectors can be resolved into x and y components using trigonometry.
3) Vector addition and multiplication using graphical and numerical methods including dot products and cross products.
control charts
Control charts are graphic tools used to detect unusual variations in a production process. There are different types of control charts for variables, including X-bar charts, R charts, and σ charts. X-bar charts monitor the average quality, R charts monitor variability between samples, and σ charts provide a better picture of variations. The charts contain a central line for the average or mean and upper and lower control limits calculated using statistical formulas. Data is plotted and checked against the control limits to determine if the production process is in statistical control.
Rectangular Coordinate System II
This document discusses key concepts related to the rectangular coordinate system:
- It aims to summarize concepts of the Cartesian plane, explain its real-life uses, and demonstrate its representation through shapes and maps.
- It reviews plotting points on the Cartesian plane by providing examples of completing sentences with the correct coordinate system terms like axes, quadrants, and ordered pairs.
- It explains how to identify the quadrant a point is located in based on the signs of its x- and y-coordinates.
- It poses assignment questions about linear equations in two variables, including how to determine if an ordered pair is a solution to such an equation.
1150 day 11
Ratios, proportions, and percents can be used to compare quantities and solve problems. A ratio compares two quantities, like the number of squares to circles. Equal ratios form a proportion, which can be used to solve for unknown values. Percents represent a number out of 100. Common percent calculations include finding a percent of a number and converting between fractions, decimals, and percents. The percent proportion states that the percent equals the part divided by the whole quantity.
1150 day 10
This document covers topics related to repeating decimals, irrational numbers, and square roots. It includes examples of writing repeating decimals as fractions, ordering decimals, finding square roots, and using the Pythagorean theorem. Various math problems are presented along with step-by-step solutions to illustrate these concepts.
1150 day 9
1) Decimals represent numbers using place value with decimal points. To write decimals in expanded form, they are broken into place value terms using positive and negative exponents.
2) Fractions can be converted to decimals using division or by writing the fraction as a ratio of two numbers and setting up a proportion to solve for the decimal.
3) Scientific notation is used to write very large or small numbers in a standard form, such as 3.603 x 107. Operations can be done on decimals by lining up the decimal points or moving them with multiplication/division.
More Related Content
What's hot
Coordinate Plane[1]
The coordinate plane is formed by two perpendicular number lines intersecting at their zero points. It is divided into four quadrants by the x-axis and y-axis. An ordered pair (x, y) assigns a point's location by its x and y coordinates. To plot a point, start at the origin and locate the x value on the x-axis, then move up or down to the y value.
6th Math (C2) - Lesson 41--Dec15
This document contains instructions for assignment set 41 that is due tomorrow. It reviews the distributive property of multiplication over addition using examples like 3(2 + 5) and provides 5 practice problems: A) finding the area of a rectangle, B) evaluating a multiplication expression, C) simplifying 6(20 - 5) in 2 ways, D) simplifying 2(n + 5), and E) writing 2 formulas for finding the perimeter of a rectangle.
Ch6.3 Point-Slope Form
This document discusses point-slope form for writing the equation of a line given a point and slope. It provides examples of writing equations of lines using point-slope form, including lines with a given slope that pass through a point, lines that pass through two given points, lines parallel or perpendicular to another line that pass through a given point, and converting an equation in point-slope form to slope-intercept form. Exercises are provided from page 256 problems 3 through 20.
Mth 518 report grapes_garachico
GRAPES is software that allows users to draw and manipulate graphs of functions, relations, curves, and other mathematical objects. It has tools for inputting and editing functions and relations, operating on graphs by changing parameters or dragging points, and analyzing functions through tools like the function value window or definite integral window. The document provides examples of using GRAPES to draw and explore properties of linear and quadratic equations, converting between slope-intercept form and general form for lines, and using the quadratic formula to solve quadratic equations.
5.4 Slope Intercept Form
The document provides an overview of slope-intercept form for linear equations. It defines slope as the constant rate of change and the y-intercept as the y-value when x=0. Slope-intercept form is given as y=mx+b, where m is the slope and b is the y-intercept. This form can be used to graph lines, find points, and describe situations with a constant rate of change. Understanding slope-intercept form is important for showing what y-values occur at different x-values for a linear relationship.
anova Statistical analysis
1) The document discusses various statistical analysis techniques including data tabulation, graphical representation, standard deviation, ANOVA, and linear regression analysis.
2) Data tabulation involves arranging data in logical tables to reduce space, explanations, and help with comparisons. Graphical representation involves using charts like linear, bar, and pie charts to visually depict relationships.
3) Standard deviation and standard error are discussed as measures of dispersion in a data series and sampling distribution respectively. ANOVA and linear regression are analyzed as methods to understand relationships between variables and predict outcomes.
2.5 Equations of Lines
This document discusses equations of lines, including linear functions and their standard, point-slope, and slope-intercept forms. It defines parallel and perpendicular lines based on their slopes. It provides examples of writing the equation of a line from its graph or from a point and slope. Key steps include calculating the slope, selecting a point, and writing the equation in the appropriate form.
Coordinate Plane
The document defines and explains the key elements of the coordinate plane, including the x and y axes which intersect at the origin (0,0) to form four quadrants. Points on the plane are represented by coordinates (x,y) and are plotted by starting at the origin and moving right along the x-axis and up/down along the y-axis. The quadrants are numbered I through IV based on whether the x and y values are positive or negative.
Coordinate Plane Review
The document discusses key concepts about the coordinate plane, including:
1) Plotting points on the coordinate plane using ordered pairs like (1,1) and identifying which quadrant points fall into.
2) The coordinate plane is divided into four quadrants based on whether the x and y values are positive or negative.
3) Transformations like translations can change the position of shapes on the coordinate plane by sliding or shifting them along the x- or y-axis.
Md university cmis 102 week 3 hands
cmis 102 homework 3 new,cmis 102 week 3 hands on lab new,md university cmis 102,cmis 102,md university cmis 102 week 3 tutorial,cmis 102 week 3 assignment,md university cmis 102 week 3 help
Coordinate plane
The document discusses graphing ordered pairs on a coordinate plane. It defines key terms like coordinate, plane, axes, quadrants, and ordered pairs. It explains that the x-axis is horizontal, the y-axis is vertical, and they intersect at the origin (0,0). Ordered pairs use the format (x,y) to locate points by giving the x-coordinate first and y-coordinate second. Several examples are given to demonstrate graphing points in the quadrants of the coordinate plane.
Math presentation2551
The document provides steps to find lines parallel and perpendicular to the given line 2x - 3y = 9 through the point (4, -1). It is given that the slope of the original line is 2/3. The parallel line has the same slope of 2/3, while the perpendicular line has the slope of the negative reciprocal -3/2. Equations for both the parallel and perpendicular lines through the given point are provided.
Intro to coordinate plane
Into to the Coordiante Plane Lesson-Fred Jones-Teach to the eyes example.
Mathematics
Goes to the Holt Course 2 Book.
Algebra booklet
This document provides an introduction to algebra and quadratic expressions and equations, including definitions of key terms like variables, coefficients, and algebraic expressions. It covers topics like expanding, simplifying, and factorizing quadratic expressions using various methods. Real-world applications of quadratic equations are discussed, such as their use in physics, finance, and everyday contexts involving areas, profits, speeds, lenses, and mirrors.
Cartesian coordinate plane
The document discusses the Cartesian coordinate plane and functions. It defines the Cartesian plane as being formed by two perpendicular number lines called the x-axis and y-axis that intersect at the origin (0,0). It describes how each point on the plane is associated with an ordered pair (x,y) denoting its coordinates and how the plane is divided into four quadrants. It then demonstrates how to plot various points on the plane by starting at the origin and moving right or left along the x-axis and up or down along the y-axis. Finally, it discusses relations and functions, defining a function as a relation where each x-value is mapped to only one y-value.
Applied Calculus: An introduction about Real Numbers and Real Line
Lecture #: 01: "An introduction about Real Numbers & Real Line" with in a course on Applied Calculus offered at Faculty of Engineering, University of Central Punjab
By: Prof. Muhammad Rafiq.
Ap Physics C Mathematical Concepts Vectors
This document covers mathematical concepts related to AP Physics C including:
1) Polynomials of different orders and their graphs.
2) Trigonometry definitions and relationships using right triangles.
3) Vectors having both direction and magnitude, while scalars have only magnitude. Vectors can be resolved into x and y components using trigonometry.
3) Vector addition and multiplication using graphical and numerical methods including dot products and cross products.
control charts
Control charts are graphic tools used to detect unusual variations in a production process. There are different types of control charts for variables, including X-bar charts, R charts, and σ charts. X-bar charts monitor the average quality, R charts monitor variability between samples, and σ charts provide a better picture of variations. The charts contain a central line for the average or mean and upper and lower control limits calculated using statistical formulas. Data is plotted and checked against the control limits to determine if the production process is in statistical control.
Rectangular Coordinate System II
This document discusses key concepts related to the rectangular coordinate system:
- It aims to summarize concepts of the Cartesian plane, explain its real-life uses, and demonstrate its representation through shapes and maps.
- It reviews plotting points on the Cartesian plane by providing examples of completing sentences with the correct coordinate system terms like axes, quadrants, and ordered pairs.
- It explains how to identify the quadrant a point is located in based on the signs of its x- and y-coordinates.
- It poses assignment questions about linear equations in two variables, including how to determine if an ordered pair is a solution to such an equation.
What's hot (19)
Applied Calculus: An introduction about Real Numbers and Real Line
Applied Calculus: An introduction about Real Numbers and Real Line
More from Carol Defreese
1150 day 11
Ratios, proportions, and percents can be used to compare quantities and solve problems. A ratio compares two quantities, like the number of squares to circles. Equal ratios form a proportion, which can be used to solve for unknown values. Percents represent a number out of 100. Common percent calculations include finding a percent of a number and converting between fractions, decimals, and percents. The percent proportion states that the percent equals the part divided by the whole quantity.
1150 day 10
This document covers topics related to repeating decimals, irrational numbers, and square roots. It includes examples of writing repeating decimals as fractions, ordering decimals, finding square roots, and using the Pythagorean theorem. Various math problems are presented along with step-by-step solutions to illustrate these concepts.
1150 day 9
1) Decimals represent numbers using place value with decimal points. To write decimals in expanded form, they are broken into place value terms using positive and negative exponents.
2) Fractions can be converted to decimals using division or by writing the fraction as a ratio of two numbers and setting up a proportion to solve for the decimal.
3) Scientific notation is used to write very large or small numbers in a standard form, such as 3.603 x 107. Operations can be done on decimals by lining up the decimal points or moving them with multiplication/division.
1150 day 8
This document provides an overview of rational numbers including:
- Integers and fractions written in the form a/b where a and b are integers and b ≠ 0
- Equivalent fractions represented by the same number
- Ordering and comparing rational numbers
- Converting between improper fractions and mixed numbers
- Basic operations of addition, subtraction, multiplication, and division of rational numbers
- Word problems involving rational numbers
1150 day 7
This document discusses prime and composite numbers, greatest common divisors (GCD), and least common multiples (LCM). It provides examples of finding the GCD and LCM of various numbers using different methods like the intersection of sets method, prime factorization method, and Euclidean algorithm. Key definitions include: a prime number has exactly two distinct positive divisors, a composite number has factors other than itself and 1, the GCD is the largest integer that divides numbers, and the LCM is the smallest number that is a multiple of the given numbers.
1150 day 6
Integers include positive and negative whole numbers. Absolute value is the distance from zero. Addition and subtraction on a number line involve moving left or right. Multiplication follows patterns based on sign. Division is the inverse of multiplication regarding sign. A number is divisible by another if it can be written as a product of an integer multiple. Divisibility tests identify patterns in a number's digits.
1150 day 5
Algebraic thinking involves recognizing patterns, modeling situations with symbols, and analyzing change. It relies on understanding variables to represent unknown quantities. The document traces the evolution of algebraic thinking from simple equations to more complex concepts like functions, composite functions, and properties of equations. It provides examples of how algebraic reasoning and symbols can be used to represent and solve real-world problems.
1150 day 4
The document discusses various aspects of whole number operations including:
1) Place value systems and how numbers are represented in bases other than 10 such as base 5 and base 12.
2) Algorithms for addition, subtraction, multiplication, and division using various models and representations.
3) Properties of operations like the commutative, associative, identity, and zero properties of multiplication.
1150 day 3
The document discusses different number systems used throughout history including Hindu-Arabic, Egyptian, Babylonian, Mayan, and Roman systems. It also covers basic concepts of whole numbers such as addition, subtraction, and their properties. Different models are presented to demonstrate whole number operations including set, number line, take-away, comparison, and missing addend models.
1150 day 2
The document discusses sets and set operations including defining sets, elements, cardinal and ordinal numbers, equal and equivalent sets, subsets, Venn diagrams, and set operations like union, intersection, and complement. Examples are provided to illustrate concepts like finite and infinite sets, subsets, Venn diagrams representing multiple sets and operations, and using Venn diagrams to solve problems involving sets and their relationships.
1150 day 1
The number of terms in each sequence can be determined by finding a one-to-one correspondence with the counting numbers.
Alg2 lesson 13-5
This document discusses solving an ambiguous triangle where it is not a right triangle and the measures of angles and sides are not fully known. It determines that trigonometric functions and the Law of Sines cannot be used. It identifies that the Law of Cosines is the appropriate theorem to use to begin solving since it requires only knowing the measures of three sides.
Alg2 lesson 13-4
The document discusses solving for unknown sides and angles of triangles using trigonometric functions like the law of sines. Several multi-step example problems are worked through that involve determining if a triangle is possible based on given information, finding missing side lengths, and calculating angles. Diagrams are included to illustrate each step of the example problems.
Alg2 lesson 13-3
The document contains instructions for finding trigonometric function values given specific angle measurements or terminal side locations. It includes:
1) Finding the six trig functions of an angle with a terminal side at (8, -15)
2) Finding the six trig functions of an angle with a terminal side at (-3, 4)
3) Finding the reference angle of 330°
4) Finding the reference angle of an angle in Quadrant III
5) Finding the value of sin(135°)
6) Finding the remaining five trig functions of an angle in Quadrant III with a terminal side of (-4, -3)
Alg2 lesson 13-3
The document contains instructions for finding trigonometric function values given specific angle measurements or terminal side locations. It includes:
1) Finding the six trig functions of an angle with a terminal side at (8, -15)
2) Finding the six trig functions of an angle with a terminal side at (-3, 4)
3) Finding the reference angle of 330°
4) Finding the reference angle of an angle in Quadrant III
5) Finding the value of sin(135°)
6) Finding the remaining five trig functions of an angle in Quadrant III with a terminal side of (-4, -3)
Alg2 lesson 13-2
The document describes how to draw angles in standard position on a unit circle and convert between degrees and radians. It provides examples of drawing angles such as 210°, -45°, and 540° in standard position and rewriting angles such as 30°, 45°, and an unspecified angle in radians and degrees. It also gives examples of finding coterminal angles for 210° with one positive and one negative measure.
Alg2 lesson 13-1
This document discusses trigonometric functions and their ratios, including sine, cosine, tangent, cosecant, secant, and cotangent. It provides examples of using trigonometric functions to solve values in right triangles, including finding missing side lengths and angle measures. Special right triangles with ratios of 1/2, 1/√3, and 1/√2 are also covered.
Alg2 lesson 11-2 and 11-4
The document provides information about arithmetic and geometric series. It defines arithmetic and geometric series, provides examples of finding sums of arithmetic series using formulas, and defines the key terms (first term, common ratio, number of terms, last term) used in the formula to calculate the sum of a geometric series.
Alg2 lesson 11-3
The document discusses geometric sequences, which are patterns of numbers where each term is found by multiplying the previous term by a constant called the common ratio. It provides examples of geometric sequences with different common ratios and shows how to write equations to find the nth term in a sequence. It also explains how to find specific terms in a geometric sequence and calculates the geometric means between two nonconsecutive terms.
Alg2 lesson 11-1
The document discusses arithmetic sequences, which are patterns of numbers where each term is found by adding a constant value to the previous term. It provides examples of arithmetic sequences with different common differences and shows how to write equations to determine the nth term. It also explains how to find terms within an arithmetic sequence and determine arithmetic means between two non-consecutive terms.
More from Carol Defreese (20)
Recently uploaded
Chapter wise All Notes of First year Basic Civil Engineering.pptx
Chapter wise All Notes of First year Basic Civil Engineering
Syllabus
Chapter-1
Introduction to objective, scope and outcome the subject
Chapter 2
Introduction: Scope and Specialization of Civil Engineering, Role of civil Engineer in Society, Impact of infrastructural development on economy of country.
Chapter 3
Surveying: Object Principles & Types of Surveying; Site Plans, Plans & Maps; Scales & Unit of different Measurements.
Linear Measurements: Instruments used. Linear Measurement by Tape, Ranging out Survey Lines and overcoming Obstructions; Measurements on sloping ground; Tape corrections, conventional symbols. Angular Measurements: Instruments used; Introduction to Compass Surveying, Bearings and Longitude & Latitude of a Line, Introduction to total station.
Levelling: Instrument used Object of levelling, Methods of levelling in brief, and Contour maps.
Chapter 4
Buildings: Selection of site for Buildings, Layout of Building Plan, Types of buildings, Plinth area, carpet area, floor space index, Introduction to building byelaws, concept of sun light & ventilation. Components of Buildings & their functions, Basic concept of R.C.C., Introduction to types of foundation
Chapter 5
Transportation: Introduction to Transportation Engineering; Traffic and Road Safety: Types and Characteristics of Various Modes of Transportation; Various Road Traffic Signs, Causes of Accidents and Road Safety Measures.
Chapter 6
Environmental Engineering: Environmental Pollution, Environmental Acts and Regulations, Functional Concepts of Ecology, Basics of Species, Biodiversity, Ecosystem, Hydrological Cycle; Chemical Cycles: Carbon, Nitrogen & Phosphorus; Energy Flow in Ecosystems.
Water Pollution: Water Quality standards, Introduction to Treatment & Disposal of Waste Water. Reuse and Saving of Water, Rain Water Harvesting. Solid Waste Management: Classification of Solid Waste, Collection, Transportation and Disposal of Solid. Recycling of Solid Waste: Energy Recovery, Sanitary Landfill, On-Site Sanitation. Air & Noise Pollution: Primary and Secondary air pollutants, Harmful effects of Air Pollution, Control of Air Pollution. . Noise Pollution Harmful Effects of noise pollution, control of noise pollution, Global warming & Climate Change, Ozone depletion, Greenhouse effect
Text Books:
1. Palancharmy, Basic Civil Engineering, McGraw Hill publishers.
2. Satheesh Gopi, Basic Civil Engineering, Pearson Publishers.
3. Ketki Rangwala Dalal, Essentials of Civil Engineering, Charotar Publishing House.
4. BCP, Surveying volume 1
What is Digital Literacy? A guest blog from Andy McLaughlin, University of Ab...
What is Digital Literacy? A guest blog from Andy McLaughlin, University of Aberdeen
Pengantar Penggunaan Flutter - Dart programming language1.pptx
Pengantar Penggunaan Flutter - Dart programming language1.pptx
clinical examination of hip joint (1).pdf
described clinical examination all orthopeadic conditions .
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UP
This Dissertation explores the particular circumstances of Mirzapur, a region located in the
core of India. Mirzapur, with its varied terrains and abundant biodiversity, offers an optimal
environment for investigating the changes in vegetation cover dynamics. Our study utilizes
advanced technologies such as GIS (Geographic Information Systems) and Remote sensing to
analyze the transformations that have taken place over the course of a decade.
The complex relationship between human activities and the environment has been the focus
of extensive research and worry. As the global community grapples with swift urbanization,
population expansion, and economic progress, the effects on natural ecosystems are becoming
more evident. A crucial element of this impact is the alteration of vegetation cover, which plays a
significant role in maintaining the ecological equilibrium of our planet.Land serves as the foundation for all human activities and provides the necessary materials for
these activities. As the most crucial natural resource, its utilization by humans results in different
'Land uses,' which are determined by both human activities and the physical characteristics of the
land.
The utilization of land is impacted by human needs and environmental factors. In countries
like India, rapid population growth and the emphasis on extensive resource exploitation can lead
to significant land degradation, adversely affecting the region's land cover.
Therefore, human intervention has significantly influenced land use patterns over many
centuries, evolving its structure over time and space. In the present era, these changes have
accelerated due to factors such as agriculture and urbanization. Information regarding land use and
cover is essential for various planning and management tasks related to the Earth's surface,
providing crucial environmental data for scientific, resource management, policy purposes, and
diverse human activities.
Accurate understanding of land use and cover is imperative for the development planning
of any area. Consequently, a wide range of professionals, including earth system scientists, land
and water managers, and urban planners, are interested in obtaining data on land use and cover
changes, conversion trends, and other related patterns. The spatial dimensions of land use and
cover support policymakers and scientists in making well-informed decisions, as alterations in
these patterns indicate shifts in economic and social conditions. Monitoring such changes with the
help of Advanced technologies like Remote Sensing and Geographic Information Systems is
crucial for coordinated efforts across different administrative levels. Advanced technologies like
Remote Sensing and Geographic Information Systems
9
Changes in vegetation cover refer to variations in the distribution, composition, and overall
structure of plant communities across different temporal and spatial scales. These changes can
occur natural.
South African Journal of Science: Writing with integrity workshop (2024)
South African Journal of Science: Writing with integrity workshop (2024)Academy of Science of South Africa
A workshop hosted by the South African Journal of Science aimed at postgraduate students and early career researchers with little or no experience in writing and publishing journal articles.Hindi varnamala | hindi alphabet PPT.pdf
हिंदी वर्णमाला पीपीटी, hindi alphabet PPT presentation, hindi varnamala PPT, Hindi Varnamala pdf, हिंदी स्वर, हिंदी व्यंजन, sikhiye hindi varnmala, dr. mulla adam ali, hindi language and literature, hindi alphabet with drawing, hindi alphabet pdf, hindi varnamala for childrens, hindi language, hindi varnamala practice for kids, https://www.drmullaadamali.com
Traditional Musical Instruments of Arunachal Pradesh and Uttar Pradesh - RAYH...
Traditional Musical Instruments of Arunachal Pradesh and Uttar Pradesh
Advanced Java[Extra Concepts, Not Difficult].docx
This is part 2 of my Java Learning Journey. This contains Hashing, ArrayList, LinkedList, Date and Time Classes, Calendar Class and more.
Main Java[All of the Base Concepts}.docx
This is part 1 of my Java Learning Journey. This Contains Custom methods, classes, constructors, packages, multithreading , try- catch block, finally block and more.
How to deliver Powerpoint Presentations.pptx
"How to make and deliver dynamic presentations by making it more interactive to captivate your audience attention"
PCOS corelations and management through Ayurveda.
This presentation includes basic of PCOS their pathology and treatment and also Ayurveda correlation of PCOS and Ayurvedic line of treatment mentioned in classics.
How to Create a More Engaging and Human Online Learning Experience
How to Create a More Engaging and Human Online Learning Experience Wahiba Chair Training & Consulting
Wahiba Chair's Talk at the 2024 Learning Ideas Conference. BÀI TẬP BỔ TRỢ TIẾNG ANH LỚP 9 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2024-2025 - ...
BÀI TẬP BỔ TRỢ TIẾNG ANH LỚP 9 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2024-2025 - ...Nguyen Thanh Tu Collection
https://app.box.com/s/tacvl9ekroe9hqupdnjruiypvm9rdaneBÀI TẬP BỔ TRỢ TIẾNG ANH 8 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2023-2024 (CÓ FI...
BÀI TẬP BỔ TRỢ TIẾNG ANH 8 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2023-2024 (CÓ FI...Nguyen Thanh Tu Collection
https://app.box.com/s/y977uz6bpd3af4qsebv7r9b7s21935vdRecently uploaded (20)
Chapter wise All Notes of First year Basic Civil Engineering.pptx
Chapter wise All Notes of First year Basic Civil Engineering.pptx
What is Digital Literacy? A guest blog from Andy McLaughlin, University of Ab...
What is Digital Literacy? A guest blog from Andy McLaughlin, University of Ab...
Pengantar Penggunaan Flutter - Dart programming language1.pptx
Pengantar Penggunaan Flutter - Dart programming language1.pptx
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UP
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UP
South African Journal of Science: Writing with integrity workshop (2024)
South African Journal of Science: Writing with integrity workshop (2024)
NEWSPAPERS - QUESTION 1 - REVISION POWERPOINT.pptx
NEWSPAPERS - QUESTION 1 - REVISION POWERPOINT.pptx
Traditional Musical Instruments of Arunachal Pradesh and Uttar Pradesh - RAYH...
Traditional Musical Instruments of Arunachal Pradesh and Uttar Pradesh - RAYH...
Liberal Approach to the Study of Indian Politics.pdf
Liberal Approach to the Study of Indian Politics.pdf
How to Create a More Engaging and Human Online Learning Experience
How to Create a More Engaging and Human Online Learning Experience
BÀI TẬP BỔ TRỢ TIẾNG ANH LỚP 9 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2024-2025 - ...
BÀI TẬP BỔ TRỢ TIẾNG ANH LỚP 9 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2024-2025 - ...
BÀI TẬP BỔ TRỢ TIẾNG ANH 8 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2023-2024 (CÓ FI...
BÀI TẬP BỔ TRỢ TIẾNG ANH 8 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2023-2024 (CÓ FI...
Alg2 Graphing Rational Functions (One More)
- 1. Graph
- 2. Graph Graphing a rational function: a step-by-step example
- 3. Graph Step 1: factor
- 4. Graph Step 1: factor
- 5. Graph Step 2: simplify
- 6. Graph Step 2: simplify vertical asymptote: x = –3
- 7. Graph Step 2: simplify Hole: ( 2, 1) vertical asymptote: x = –3 How to find the y-coordinate:
- 8. Graph Step 3: Horizontal asymptote Look at highest-degree terms Same degree Compare leading coefficients Horizontal asymptote:
- 9. Graph Step 4: Find more points by making a table of values x y -6 -5 -4 -3 -2 -1 0 11/3 9/2 7/1 VA -3/1 -1/2 1/3