Chapter 3.4
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Logarithmic functions have several key properties including that they are the inverses of exponential functions, their graphs result in curves that are always increasing but approach horizontal asymptotes, and they satisfy certain algebraic rules when transformed from one base to another through change of base formulas.
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Chapter 3.4
Logarithmic functions have several key properties including change of base which allows converting between different logarithmic bases, and their behavior when graphed results in a curve that slowly levels off but never intersects the horizontal axis. Logarithmic functions are useful in many areas of science, engineering, and mathematics for modeling exponential growth and decay.
Section 1.1
The document discusses mathematical modeling and functions. It defines mathematical modeling as using mathematical structures to approximate real-world phenomena in order to study or predict behavior. It then discusses different types of mathematical models like numerical, algebraic and graphical models. The rest of the document focuses on defining and representing functions, including discussing domain and range, and ways to find the domain of a function either algebraically or graphically. It concludes by listing specific homework problems.
2.1 lesson
This document discusses different types of real numbers including rational numbers, irrational numbers, integers, and whole numbers. It defines rational numbers and discusses their properties such as opposites and absolute value. It also explains what conditional statements are, noting they have a hypothesis and conclusion in an "if-then" format and can be proven true or false with a counterexample. Examples of conditional statements involving rational numbers and absolute value are provided. Students are assigned practice problems from lessons 2.2, 2.3, and 2.4.
Unit 4.4
This document discusses sinusoidal functions and their graphs. It defines a sinusoid as a function of the form f(x) = asin(bx + c) + d, where a, b, c, and d are constants. It describes key characteristics of sinusoidal graphs, including amplitude, period, frequency, and how phase shifts and vertical/horizontal transformations alter the graph. Examples are provided to illustrate determining these characteristics from equations and sketching sinusoidal graphs.
Unit 4.1
This document discusses angles and their measurement. It explains that angles are measured in degrees, with a full circle being 360 degrees, or radians, where the radian measure is based on arc length. It provides examples of converting between degrees and radians. It also discusses measuring angular motion in revolutions per minute versus linear motion in miles per hour or feet per second. Circumference and arc length formulas are presented using both degree and radian measures.
Detailed Lesson Plan (ENGLISH, MATH, SCIENCE, FILIPINO)
Thanks everybody! The lesson plans presented were actually outdated and can still be improved. I was also a college student when I did these. There were minor errors but the important thing is, the structure and flow of activities (for an hour-long class) are included here. I appreciate all of your comments! Please like my fan page on facebook search for JUNNIE SALUD.
*The detailed LP for English is from Ms. Juliana Patricia Tenzasas. I just revised it a little.
For questions about education-related matters, you can directly email me at mr_junniesalud@yahoo.com
Section 4.2
This document provides homework assignments from a math textbook. Students are assigned problems on vertex form and intercept form of graphs from pages 240-245 with problems #5, 21-31 odd, 33, 35, 44-46, 57, 60. Additional problems on the same topics are assigned from pages 249-251 including problems #13-21 odd, 25-41 odd, and 54.
Section 4.1
This section discusses properties of quadratic functions including their graphs, minimum and maximum values, and axis of symmetry. It covers labeling key features such as the vertex on the graph of a quadratic function in standard form and identifying the axis of symmetry.
Recommended
Chapter 3.4
Logarithmic functions have several key properties including change of base which allows converting between different logarithmic bases, and their behavior when graphed results in a curve that slowly levels off but never intersects the horizontal axis. Logarithmic functions are useful in many areas of science, engineering, and mathematics for modeling exponential growth and decay.
Section 1.1
The document discusses mathematical modeling and functions. It defines mathematical modeling as using mathematical structures to approximate real-world phenomena in order to study or predict behavior. It then discusses different types of mathematical models like numerical, algebraic and graphical models. The rest of the document focuses on defining and representing functions, including discussing domain and range, and ways to find the domain of a function either algebraically or graphically. It concludes by listing specific homework problems.
2.1 lesson
This document discusses different types of real numbers including rational numbers, irrational numbers, integers, and whole numbers. It defines rational numbers and discusses their properties such as opposites and absolute value. It also explains what conditional statements are, noting they have a hypothesis and conclusion in an "if-then" format and can be proven true or false with a counterexample. Examples of conditional statements involving rational numbers and absolute value are provided. Students are assigned practice problems from lessons 2.2, 2.3, and 2.4.
Unit 4.4
This document discusses sinusoidal functions and their graphs. It defines a sinusoid as a function of the form f(x) = asin(bx + c) + d, where a, b, c, and d are constants. It describes key characteristics of sinusoidal graphs, including amplitude, period, frequency, and how phase shifts and vertical/horizontal transformations alter the graph. Examples are provided to illustrate determining these characteristics from equations and sketching sinusoidal graphs.
Unit 4.1
This document discusses angles and their measurement. It explains that angles are measured in degrees, with a full circle being 360 degrees, or radians, where the radian measure is based on arc length. It provides examples of converting between degrees and radians. It also discusses measuring angular motion in revolutions per minute versus linear motion in miles per hour or feet per second. Circumference and arc length formulas are presented using both degree and radian measures.
Detailed Lesson Plan (ENGLISH, MATH, SCIENCE, FILIPINO)
Thanks everybody! The lesson plans presented were actually outdated and can still be improved. I was also a college student when I did these. There were minor errors but the important thing is, the structure and flow of activities (for an hour-long class) are included here. I appreciate all of your comments! Please like my fan page on facebook search for JUNNIE SALUD.
*The detailed LP for English is from Ms. Juliana Patricia Tenzasas. I just revised it a little.
For questions about education-related matters, you can directly email me at mr_junniesalud@yahoo.com
Section 4.2
This document provides homework assignments from a math textbook. Students are assigned problems on vertex form and intercept form of graphs from pages 240-245 with problems #5, 21-31 odd, 33, 35, 44-46, 57, 60. Additional problems on the same topics are assigned from pages 249-251 including problems #13-21 odd, 25-41 odd, and 54.
Section 4.1
This section discusses properties of quadratic functions including their graphs, minimum and maximum values, and axis of symmetry. It covers labeling key features such as the vertex on the graph of a quadratic function in standard form and identifying the axis of symmetry.
Section 2 and 3
This document discusses power functions and variation, analyzing power functions, monomial functions, end behavior, even or odd functions, terminology, and graphs facts. It states that a polynomial function of degree n has at most n - 1 local extrema and at most n zeros. It also notes that the graph of a polynomial function of degree n has at most n - 1 turns and that the zeros of the function are the x-intercepts of its corresponding graph.
Section 1
This document discusses different types of polynomial functions including zero functions, constant functions, linear functions, quadratic functions, and how to find the equation of a linear function using average rate of change. It also covers key aspects of quadratic functions such as their form and degree.
Section 1.5
Parametric equations allow functions to be defined using a third variable t, called a parameter, to define both x and y values. For example, a function can be defined parametrically as x=f(t) and y=g(t). Inverse functions relate each element of an ordered pair (x,y) to another ordered pair by reflecting points across the line y=x. This is known as the inverse reflection principle. Inverse functions satisfy the horizontal line test, meaning each x value corresponds to only one y value.
2.5 2.6 lesson
The document discusses applying the distributive property to algebraic expressions by breaking them down into terms, coefficients, and constants and then combining like terms. It provides examples of distributing multiplication over addition in expressions like 4(y+3), n(n-9), and -2(x+7). It also covers simplifying expressions involving subtraction, multiplication of terms with variables and numbers, and division of real numbers. The homework assigned is to complete odd problems from pages 99-100 and all problems from pages 106-107.
Section 1.3
This document discusses graphing the 12 basic functions in mathematics. It provides an example of graphing the 12 basic functions and mentions that graphing these functions is an example. The document repeats the phrase "Graph the 12 Basic Functions" three times.
Alg 2 sections 2.1
This document discusses relations and functions. It defines a relation as a mapping or pairing of input and output values, with the input set called the domain and output set called the range. Relations can be represented through tables, mapping diagrams, ordered pairs, and graphs. The document defines a function as a special type of relation where each input has exactly one output; if any input has more than one output it is not a function. Examples of functions and non-functions are provided. Homework problems from the textbook are listed at the end.
Section 1.1
The document discusses mathematical modeling and functions. It defines a mathematical model as a structure that approximates real-world phenomena to study or predict behavior. It then discusses numerical, algebraic and graphical models. It also discusses functions, including defining them, representing them with equations, graphs and mappings, and determining their domains and ranges. It provides examples of finding domains and ends with homework problems assigned.
Alg2 section 1.7
This document discusses how to solve absolute value equations and inequalities in 3 sections: the first section explains absolute value, the second section provides instructions for solving absolute value equations, and the third section gives directions for solving absolute value inequalities and includes an application example.
Pa section 1.6
The document defines and provides examples of calculating the median, mode, and range of data sets. It explains that the median is the middle value of a data set in numerical order, or the mean of the two middle values for an even number of values. The mode is the value that occurs most frequently. The range is the difference between the greatest and least values. Examples are provided to demonstrate calculating each metric for temperature and score data sets.
Pa section 1.6
The document defines and provides examples of calculating the median, mode, and range of data sets. It explains that the median is the middle value of a data set in numerical order, or the mean of the two middle values for an even number of values. The mode is the value that occurs most frequently in a data set. The range is the difference between the greatest and least values. Examples are given of calculating each for a set of monthly temperature data.
Alg 2 section 1.6
The document discusses solving linear inequalities and includes three topics: forms of linear inequalities, compound inequalities, and homework assigned which includes odd numbered problems 23 through 33 and 37 through 47 on page 45 of the text.
Pc sections p.6-p.7
This document lists key properties of numbers and operations covered in two sections. Section P.6 covers commutative and associative properties of addition and multiplication as well as the distributive property of multiplication over addition and subtraction. Section P.7 directs students to complete specific math problems from two different pages focusing on odd numbered questions.
Alg 1 sections 1.5-1.6
1. This document discusses different ways to represent functions including equations, tables, and mapping diagrams. It provides examples of each.
2. Strategies for solving problems are outlined, including using formulas, patterns, and drawing diagrams. Specific math problems are provided as examples.
3. Homework assignments are listed at the end, including problem numbers from pages 31-32 and 38-39.
Alg2 sections 1.4-1.5
This document provides an overview of rewriting formulas and equations. It includes sections on common formulas, solving for variables, examples to practice, and application problems. Formulas covered include distance, temperature, areas of shapes, and circumference. It also discusses strategies for problem solving like using formulas, patterns, and diagrams. Sample problems are provided for average speed, finding heights from a pattern, and positioning posters on a wall. The document concludes with assigned homework problems.
Pc sections p.4-p.5
This document provides an overview of topics in algebra including:
1) Different forms of equations for lines (slope-intercept, point-slope, etc.) and quadratics (general, vertex).
2) How to determine if lines are parallel or perpendicular.
3) Methods for graphing and solving linear and quadratic equations (finding intercepts, using a graphing calculator, extracting roots, using the quadratic formula).
4) An example word problem on investing money with different interest rates and determining the amount to invest to earn a target return.
5) Assigned homework problems from the textbook.
Pa sections 1-2
This document provides instructions for performing common mathematical operations like addition, subtraction, multiplication, and division. It includes examples of writing down a number and then performing sequential operations on it like doubling, adding or subtracting other numbers, dividing, and subtracting the original number. The document also lists common words used to indicate different operations and directs the reader to specific math problems to complete on designated pages.
Alg1 sections 1.1-1.2
This document summarizes key concepts from sections 1 and 2 of chapter 1 including:
- PEMDAS order of operations with parentheses, exponents, multiplication/division, addition/subtraction.
- Definitions of powers/exponents as repeated multiplication with a base and exponent.
- Examples of evaluating expressions and algebraic equations.
- Formulas for estimating a frog's jump distance, points earned in soccer, and adult height based on childhood height.
- Practice problems listed for pages 5-7 and 10-12.
Pc sections p.1-p.3
This document provides an overview of number types including real numbers, imaginary numbers, rational numbers, irrational numbers, integers, whole numbers, and natural numbers. It also covers interval notation and types of intervals. Key concepts covered include the x-axis, y-axis, origin, ordered pairs, coordinates, quadrants, absolute value, distance formula, midpoint formula, and the standard form of a circle. Practice problems are assigned from pages 9-10, 17-19, and 25-27 of the text.
Pa sections 1-2
The document provides instructions for performing mathematical operations including addition, subtraction, multiplication, and division. It lists common words and phrases used to indicate each operation, such as "add", "subtract", "double", and "divide". It then provides two examples of multi-step operations where the reader writes down a number and performs successive operations of doubling, adding, subtracting, and dividing the number.
Alg2 sections 1, 2, and3
This document provides an overview of key concepts from the first three sections of an Algebra 2 textbook. It introduces different types of real numbers like integers, rational numbers, and irrational numbers. It discusses how to plot numbers on a real number line and use the order of operations. Properties of real numbers are defined, including closure, commutative, associative, identity, inverse, and distributive. The document also covers unit analysis, numerical and algebraic expressions, solving linear equations, and key vocabulary terms. Homework problems are assigned from various textbook pages.
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Section 2 and 3
This document discusses power functions and variation, analyzing power functions, monomial functions, end behavior, even or odd functions, terminology, and graphs facts. It states that a polynomial function of degree n has at most n - 1 local extrema and at most n zeros. It also notes that the graph of a polynomial function of degree n has at most n - 1 turns and that the zeros of the function are the x-intercepts of its corresponding graph.
Section 1
This document discusses different types of polynomial functions including zero functions, constant functions, linear functions, quadratic functions, and how to find the equation of a linear function using average rate of change. It also covers key aspects of quadratic functions such as their form and degree.
Section 1.5
Parametric equations allow functions to be defined using a third variable t, called a parameter, to define both x and y values. For example, a function can be defined parametrically as x=f(t) and y=g(t). Inverse functions relate each element of an ordered pair (x,y) to another ordered pair by reflecting points across the line y=x. This is known as the inverse reflection principle. Inverse functions satisfy the horizontal line test, meaning each x value corresponds to only one y value.
2.5 2.6 lesson
The document discusses applying the distributive property to algebraic expressions by breaking them down into terms, coefficients, and constants and then combining like terms. It provides examples of distributing multiplication over addition in expressions like 4(y+3), n(n-9), and -2(x+7). It also covers simplifying expressions involving subtraction, multiplication of terms with variables and numbers, and division of real numbers. The homework assigned is to complete odd problems from pages 99-100 and all problems from pages 106-107.
Section 1.3
This document discusses graphing the 12 basic functions in mathematics. It provides an example of graphing the 12 basic functions and mentions that graphing these functions is an example. The document repeats the phrase "Graph the 12 Basic Functions" three times.
Alg 2 sections 2.1
This document discusses relations and functions. It defines a relation as a mapping or pairing of input and output values, with the input set called the domain and output set called the range. Relations can be represented through tables, mapping diagrams, ordered pairs, and graphs. The document defines a function as a special type of relation where each input has exactly one output; if any input has more than one output it is not a function. Examples of functions and non-functions are provided. Homework problems from the textbook are listed at the end.
Section 1.1
The document discusses mathematical modeling and functions. It defines a mathematical model as a structure that approximates real-world phenomena to study or predict behavior. It then discusses numerical, algebraic and graphical models. It also discusses functions, including defining them, representing them with equations, graphs and mappings, and determining their domains and ranges. It provides examples of finding domains and ends with homework problems assigned.
Alg2 section 1.7
This document discusses how to solve absolute value equations and inequalities in 3 sections: the first section explains absolute value, the second section provides instructions for solving absolute value equations, and the third section gives directions for solving absolute value inequalities and includes an application example.
Pa section 1.6
The document defines and provides examples of calculating the median, mode, and range of data sets. It explains that the median is the middle value of a data set in numerical order, or the mean of the two middle values for an even number of values. The mode is the value that occurs most frequently. The range is the difference between the greatest and least values. Examples are provided to demonstrate calculating each metric for temperature and score data sets.
Pa section 1.6
The document defines and provides examples of calculating the median, mode, and range of data sets. It explains that the median is the middle value of a data set in numerical order, or the mean of the two middle values for an even number of values. The mode is the value that occurs most frequently in a data set. The range is the difference between the greatest and least values. Examples are given of calculating each for a set of monthly temperature data.
Alg 2 section 1.6
The document discusses solving linear inequalities and includes three topics: forms of linear inequalities, compound inequalities, and homework assigned which includes odd numbered problems 23 through 33 and 37 through 47 on page 45 of the text.
Pc sections p.6-p.7
This document lists key properties of numbers and operations covered in two sections. Section P.6 covers commutative and associative properties of addition and multiplication as well as the distributive property of multiplication over addition and subtraction. Section P.7 directs students to complete specific math problems from two different pages focusing on odd numbered questions.
Alg 1 sections 1.5-1.6
1. This document discusses different ways to represent functions including equations, tables, and mapping diagrams. It provides examples of each.
2. Strategies for solving problems are outlined, including using formulas, patterns, and drawing diagrams. Specific math problems are provided as examples.
3. Homework assignments are listed at the end, including problem numbers from pages 31-32 and 38-39.
Alg2 sections 1.4-1.5
This document provides an overview of rewriting formulas and equations. It includes sections on common formulas, solving for variables, examples to practice, and application problems. Formulas covered include distance, temperature, areas of shapes, and circumference. It also discusses strategies for problem solving like using formulas, patterns, and diagrams. Sample problems are provided for average speed, finding heights from a pattern, and positioning posters on a wall. The document concludes with assigned homework problems.
Pc sections p.4-p.5
This document provides an overview of topics in algebra including:
1) Different forms of equations for lines (slope-intercept, point-slope, etc.) and quadratics (general, vertex).
2) How to determine if lines are parallel or perpendicular.
3) Methods for graphing and solving linear and quadratic equations (finding intercepts, using a graphing calculator, extracting roots, using the quadratic formula).
4) An example word problem on investing money with different interest rates and determining the amount to invest to earn a target return.
5) Assigned homework problems from the textbook.
Pa sections 1-2
This document provides instructions for performing common mathematical operations like addition, subtraction, multiplication, and division. It includes examples of writing down a number and then performing sequential operations on it like doubling, adding or subtracting other numbers, dividing, and subtracting the original number. The document also lists common words used to indicate different operations and directs the reader to specific math problems to complete on designated pages.
Alg1 sections 1.1-1.2
This document summarizes key concepts from sections 1 and 2 of chapter 1 including:
- PEMDAS order of operations with parentheses, exponents, multiplication/division, addition/subtraction.
- Definitions of powers/exponents as repeated multiplication with a base and exponent.
- Examples of evaluating expressions and algebraic equations.
- Formulas for estimating a frog's jump distance, points earned in soccer, and adult height based on childhood height.
- Practice problems listed for pages 5-7 and 10-12.
Pc sections p.1-p.3
This document provides an overview of number types including real numbers, imaginary numbers, rational numbers, irrational numbers, integers, whole numbers, and natural numbers. It also covers interval notation and types of intervals. Key concepts covered include the x-axis, y-axis, origin, ordered pairs, coordinates, quadrants, absolute value, distance formula, midpoint formula, and the standard form of a circle. Practice problems are assigned from pages 9-10, 17-19, and 25-27 of the text.
Pa sections 1-2
The document provides instructions for performing mathematical operations including addition, subtraction, multiplication, and division. It lists common words and phrases used to indicate each operation, such as "add", "subtract", "double", and "divide". It then provides two examples of multi-step operations where the reader writes down a number and performs successive operations of doubling, adding, subtracting, and dividing the number.
Alg2 sections 1, 2, and3
This document provides an overview of key concepts from the first three sections of an Algebra 2 textbook. It introduces different types of real numbers like integers, rational numbers, and irrational numbers. It discusses how to plot numbers on a real number line and use the order of operations. Properties of real numbers are defined, including closure, commutative, associative, identity, inverse, and distributive. The document also covers unit analysis, numerical and algebraic expressions, solving linear equations, and key vocabulary terms. Homework problems are assigned from various textbook pages.
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Chapter 3.4
- 1. CHAPTER 3.3 Properties of Logarithmic Functions
- 3. Graphs • •
- 4. Properties of Logarithmic Functions •