The document discusses parent graphs of cube root and cubic functions. It explains that the parent graph of the cube root function y=√x is a V-shape that opens to the right, and the parent graph of the cubic function y=x^3 is shaped like an upside-down V that opens downward.
This document discusses parent graphs of cubic and cube root functions. Cubic functions have a graph that is shaped like a curve opening upwards or downwards, while cube root functions have a graph that curves smoothly from left to right. Both cubic and cube root graphs pass the vertical line test and are one-to-one functions.
This document discusses right triangles on May 12, 2014. It covers right triangles and their properties over multiple pages. The key topic is right triangles and how to understand their characteristics and relationships between sides and angles.
1. The project requires students to graph the 13 parent functions and apply transformations to create child functions.
2. Students must complete a parent function foldable with information on all 13 functions and create a poster showing the graphs of each parent function and one example of a child function using a transformation.
3. The poster will be graded based on neatness, completeness of information and transformations, and visual appeal.
This document contains a math worksheet on graphing transformations of the parent function y=x. Students are asked to graph various transformations that involve shifts, stretches, shrinks, and reflections. They are also asked to describe the domain, range, intercepts, and end behavior of different transformed functions.
When dividing radicals, only the numbers outside the radicals are divided in the numerator and denominator, and the same for numbers inside radicals. This can sometimes leave a radical in the denominator, which is improper. To fix this, a process called rationalizing the denominator is used to remove radicals from the denominator. Examples are provided of dividing radicals and rationalizing denominators.
The document discusses parent graphs of cube root and cubic functions. It explains that the parent graph of the cube root function y=√x is a V-shape that opens to the right, and the parent graph of the cubic function y=x^3 is shaped like an upside-down V that opens downward.
This document discusses parent graphs of cubic and cube root functions. Cubic functions have a graph that is shaped like a curve opening upwards or downwards, while cube root functions have a graph that curves smoothly from left to right. Both cubic and cube root graphs pass the vertical line test and are one-to-one functions.
This document discusses right triangles on May 12, 2014. It covers right triangles and their properties over multiple pages. The key topic is right triangles and how to understand their characteristics and relationships between sides and angles.
1. The project requires students to graph the 13 parent functions and apply transformations to create child functions.
2. Students must complete a parent function foldable with information on all 13 functions and create a poster showing the graphs of each parent function and one example of a child function using a transformation.
3. The poster will be graded based on neatness, completeness of information and transformations, and visual appeal.
This document contains a math worksheet on graphing transformations of the parent function y=x. Students are asked to graph various transformations that involve shifts, stretches, shrinks, and reflections. They are also asked to describe the domain, range, intercepts, and end behavior of different transformed functions.
When dividing radicals, only the numbers outside the radicals are divided in the numerator and denominator, and the same for numbers inside radicals. This can sometimes leave a radical in the denominator, which is improper. To fix this, a process called rationalizing the denominator is used to remove radicals from the denominator. Examples are provided of dividing radicals and rationalizing denominators.
This document discusses dividing radicals. It states that when dividing radicals, only the numbers outside the radicals in the numerator are divided by those outside in the denominator, and the same is done for numbers inside the radicals. An example is shown where this leaves a radical in the denominator, which is improper form. The document notes that a process called rationalizing the denominator is used to remove radicals from the denominator.
This document discusses transformations of the square root function y=√x. It includes:
1) Matching equations like y=3√x and y=√x/2 to their graphs by graphing the parent function first.
2) Explaining that a negative sign in front of the square root, like y=-√x, reflects the graph over the x-axis.
3) Having students work in groups to draw transformed square root graphs, identify the transformation, and write the domain and range.
The document discusses adding and subtracting radicals. It reviews collecting like terms and then explains that to add or subtract radicals, you add the coefficients of like terms, which are radicals that have the same index and radicand. Examples are provided to demonstrate adding and subtracting radicals.
This document provides a lesson on adding and subtracting radicals. It first reviews collecting like terms when adding and subtracting expressions. It then explains that to add or subtract radicals, you add the coefficients of like terms, where like terms are radicals with the same index and radicand. Examples are provided to demonstrate adding and subtracting radicals.
The document defines and provides information about common mathematical functions including linear, quadratic, square root, cubic, cube root, absolute value, greatest integer, rational, trigonometric, exponential growth and decay, and logarithmic functions. Tables are included that specify domains, ranges, x-intercepts, and y-intercepts for each function.
The document defines and provides information about common mathematical functions including linear, quadratic, square root, cubic, cube root, absolute value, greatest integer, rational, trigonometric, exponential growth and decay, and logarithmic functions. Tables are included that specify domains, ranges, x-intercepts, and y-intercepts for each function.
1. The document discusses trigonometric ratios and how to use them to solve for missing side lengths and angle measures in right triangles.
2. It provides examples of setting up trig ratios, using the Pythagorean theorem, and using inverse trig functions to find missing angles.
3. The key steps are to label the sides of the right triangle, set up the appropriate trig ratios based on which information is known or missing, and use trig identities or the inverse functions to calculate the missing information.
This document discusses the parts of a right triangle, listing the opposite leg, adjacent leg, and hypotenuse multiple times on May 4, 2014. It focuses on the basic geometric terms for the sides of a right triangle.
This document contains a review worksheet with 35 questions covering topics in exponential and logarithmic functions including determining if equations represent exponential growth or decay, graphing functions and their inverses, evaluating logarithmic expressions with and without a calculator, solving exponential equations, and applying exponential and logarithmic concepts to word problems involving population growth, depreciation, radioactive decay, compound interest, and stock price growth.
This document contains a unit review with answers to multiple choice and free response questions about functions, inverses, logarithms, and transformations. There are 35 total problems covering topics like determining if a relationship represents a function, evaluating logarithmic expressions, and describing transformations of graphs. Tables of values are also provided for 4 functions and their inverses.
This document discusses common logarithms and how to evaluate logarithmic expressions with and without a calculator. It provides examples of rewriting exponential expressions as logarithmic expressions by setting them equal to variables and manipulating the equations. It also introduces the change of base formula for evaluating logarithms with bases other than 10.
This document contains 7 word problems about exponential growth and decay models. The problems cover topics like population growth, healthcare costs, radioactive decay, savings accounts, milk consumption, population of Washington D.C., and guppy population growth. For each problem, the student is asked to write an exponential function model, make predictions based on the model, or calculate other related values. The overall goal is to practice applying exponential functions to real-world scenarios involving growth and decay over time.
This document contains an assignment on exponential equations and logarithms. It is divided into four sections: 1) determining whether functions represent exponential growth or decay, 2) describing transformations of exponential functions, 3) graphing exponential functions and stating their domains and ranges, and 4) graphing exponential functions and their inverse logarithmic functions and stating their domains and ranges. There are 14 problems or exercises presented.
This document appears to be a log of activities that took place over two days, April 3rd and 4th, 2014. However, no specific activities or events are described within the document itself, which only repeats the date header five times without providing any additional context or information about what occurred.
This 3 sentence summary provides the high level information from the document. The document appears to be notes from a class titled "U6 day2 1st pd." that was held on April 22, 2014. It includes the title and date repeated 3 times with no other context or details provided.
The document contains a review worksheet for unit 5 with multiple questions about graphing, describing transformations of, and identifying properties of various functions. The questions include: 1) graphing and describing linear functions; 2) graphing and describing step functions; and 3) identifying asymptotes of exponential and rational functions.
This document contains a homework assignment with 4 polynomial functions that the student must graph by sketching, determine properties of like degree, whether it is odd or even, number of turns, and find any zeros, factoring when possible. The student is instructed to complete without using a graphing calculator.
This document discusses graphing polynomials and provides examples. It lists the degree, whether the polynomial is odd or even, the number of turns, whether coefficient a is positive or negative, the factored form, and the zeroes of two polynomials. The first polynomial has zeroes of -1 and 5, and the second has zeroes of 0, -3, and 2.
This document discusses dividing radicals. It states that when dividing radicals, only the numbers outside the radicals in the numerator are divided by those outside in the denominator, and the same is done for numbers inside the radicals. An example is shown where this leaves a radical in the denominator, which is improper form. The document notes that a process called rationalizing the denominator is used to remove radicals from the denominator.
This document discusses transformations of the square root function y=√x. It includes:
1) Matching equations like y=3√x and y=√x/2 to their graphs by graphing the parent function first.
2) Explaining that a negative sign in front of the square root, like y=-√x, reflects the graph over the x-axis.
3) Having students work in groups to draw transformed square root graphs, identify the transformation, and write the domain and range.
The document discusses adding and subtracting radicals. It reviews collecting like terms and then explains that to add or subtract radicals, you add the coefficients of like terms, which are radicals that have the same index and radicand. Examples are provided to demonstrate adding and subtracting radicals.
This document provides a lesson on adding and subtracting radicals. It first reviews collecting like terms when adding and subtracting expressions. It then explains that to add or subtract radicals, you add the coefficients of like terms, where like terms are radicals with the same index and radicand. Examples are provided to demonstrate adding and subtracting radicals.
The document defines and provides information about common mathematical functions including linear, quadratic, square root, cubic, cube root, absolute value, greatest integer, rational, trigonometric, exponential growth and decay, and logarithmic functions. Tables are included that specify domains, ranges, x-intercepts, and y-intercepts for each function.
The document defines and provides information about common mathematical functions including linear, quadratic, square root, cubic, cube root, absolute value, greatest integer, rational, trigonometric, exponential growth and decay, and logarithmic functions. Tables are included that specify domains, ranges, x-intercepts, and y-intercepts for each function.
1. The document discusses trigonometric ratios and how to use them to solve for missing side lengths and angle measures in right triangles.
2. It provides examples of setting up trig ratios, using the Pythagorean theorem, and using inverse trig functions to find missing angles.
3. The key steps are to label the sides of the right triangle, set up the appropriate trig ratios based on which information is known or missing, and use trig identities or the inverse functions to calculate the missing information.
This document discusses the parts of a right triangle, listing the opposite leg, adjacent leg, and hypotenuse multiple times on May 4, 2014. It focuses on the basic geometric terms for the sides of a right triangle.
This document contains a review worksheet with 35 questions covering topics in exponential and logarithmic functions including determining if equations represent exponential growth or decay, graphing functions and their inverses, evaluating logarithmic expressions with and without a calculator, solving exponential equations, and applying exponential and logarithmic concepts to word problems involving population growth, depreciation, radioactive decay, compound interest, and stock price growth.
This document contains a unit review with answers to multiple choice and free response questions about functions, inverses, logarithms, and transformations. There are 35 total problems covering topics like determining if a relationship represents a function, evaluating logarithmic expressions, and describing transformations of graphs. Tables of values are also provided for 4 functions and their inverses.
This document discusses common logarithms and how to evaluate logarithmic expressions with and without a calculator. It provides examples of rewriting exponential expressions as logarithmic expressions by setting them equal to variables and manipulating the equations. It also introduces the change of base formula for evaluating logarithms with bases other than 10.
This document contains 7 word problems about exponential growth and decay models. The problems cover topics like population growth, healthcare costs, radioactive decay, savings accounts, milk consumption, population of Washington D.C., and guppy population growth. For each problem, the student is asked to write an exponential function model, make predictions based on the model, or calculate other related values. The overall goal is to practice applying exponential functions to real-world scenarios involving growth and decay over time.
This document contains an assignment on exponential equations and logarithms. It is divided into four sections: 1) determining whether functions represent exponential growth or decay, 2) describing transformations of exponential functions, 3) graphing exponential functions and stating their domains and ranges, and 4) graphing exponential functions and their inverse logarithmic functions and stating their domains and ranges. There are 14 problems or exercises presented.
This document appears to be a log of activities that took place over two days, April 3rd and 4th, 2014. However, no specific activities or events are described within the document itself, which only repeats the date header five times without providing any additional context or information about what occurred.
This 3 sentence summary provides the high level information from the document. The document appears to be notes from a class titled "U6 day2 1st pd." that was held on April 22, 2014. It includes the title and date repeated 3 times with no other context or details provided.
The document contains a review worksheet for unit 5 with multiple questions about graphing, describing transformations of, and identifying properties of various functions. The questions include: 1) graphing and describing linear functions; 2) graphing and describing step functions; and 3) identifying asymptotes of exponential and rational functions.
This document contains a homework assignment with 4 polynomial functions that the student must graph by sketching, determine properties of like degree, whether it is odd or even, number of turns, and find any zeros, factoring when possible. The student is instructed to complete without using a graphing calculator.
This document discusses graphing polynomials and provides examples. It lists the degree, whether the polynomial is odd or even, the number of turns, whether coefficient a is positive or negative, the factored form, and the zeroes of two polynomials. The first polynomial has zeroes of -1 and 5, and the second has zeroes of 0, -3, and 2.