# Transformations of functions worksheet algebra 2 pdf

We all know that a flat mirror enables us to see an accurate image of ourselves and whatever is behind us. When we tilt the mirror, the images we see may shift horizontally or vertically.

But what happens when we bend a flexible mirror? Like a carnival funhouse mirror, it presents us with a distorted image of ourselves, stretched or compressed horizontally or vertically. In a similar way, we can distort or transform mathematical functions to better adapt them to describing objects or processes in the real world.

In this section, we will take a look at several kinds of transformations. One kind of transformation involves shifting the entire graph of a function up, down, right, or left. The simplest shift is a vertical shiftmoving the graph up or down, because this transformation involves adding a positive or negative constant to the function.

In other words, we add the same constant to the output value of the function regardless of the input. The result is a shift upward or downward. To regulate temperature in a green building, airflow vents near the roof open and close throughout the day.

During the summer, the facilities manager decides to try to better regulate temperature by increasing the amount of open vents by 20 square feet throughout the day and night. Sketch a graph of this new function. We can sketch a graph of this new function by adding 20 to each of the output values of the original function.

This will have the effect of shifting the graph vertically up. Notice that, with a vertical shift, the input values stay the same and only the output values change. For example:. As with the earlier vertical shift, notice the input values stay the same and only the output values change. Suppose the ball was instead thrown from the top of a m building. We just saw that the vertical shift is a change to the output, or outside, of the function.

We will now look at how changes to input, on the inside of the function, change its graph and meaning. A shift to the input results in a movement of the graph of the function left or right in what is known as a horizontal shift. Each input is reduced by 2 prior to squaring the function. Returning to our building airflow example from Example 2, suppose that in autumn the facilities manager decides that the original venting plan starts too late, and wants to begin the entire venting program 2 hours earlier.

Sketch a graph of the new function. Specifically, 2 shifted to 5, 4 shifted to 7, 6 shifted to 9, and 8 shifted to Function worksheets for high school students comprises a wide variety of subtopics like domain and range of a function, identifying and evaluating functions, completing tables, performing arithmetic operations on functions, composing functions, graphing linear and quadratic functions, transforming linear and quadratic functions and a lot more in a nutshell.

Sample our free worksheets from each topic. The domain and range of a function worksheets provide ample practice in determining the input and output values with exercises involving ordered pairs, tables, mapping diagrams, graphs and more. Which of the relations are functions?

## 1-5 Parent Functions and Transformations

Try to spot functions from ordered pairs, mapping diagrams, input-output tables, graphs and equations with this unit of pdf worksheets. These printable function table worksheets provide practice with different types of functions like linear, quadratic, polynomial, and more. Plug an input value in the function rule and write the output. Perform operations such as addition, subtraction, multiplication and division on functions with these function operations worksheets.

Exercises with varied levels of difficulty and revision worksheets are included here. Get your hands on these evaluating function worksheets to practice substituting input values in different types of functions like linear, quadratic, polynomial, rational, exponential, trigonometric, and piecewise to get the output.

Also, evaluate functions from graphs. Try our revision worksheets as well. Gain a thorough knowledge of composing two or three functions, evaluate functions and decomposing them as well with this array of printable composition of functions worksheets. Walk through this assortment of inverse functions worksheets, examine graphs to check if two functions are inverses of each other, find the inverses of functions, and domains with restricted domains and more.

Learn to identify and differentiate between linear and nonlinear functions from equations, graphs and tables. Graph, compare and transform linear functions and also figure out the function rule too.

Learn to find the range, compute function tables, plot the points on the grid and graph lines with this compilation of graphing linear functions worksheet pdfs curated for high-school students. Transformation of a Linear Function Worksheets. Transform a function from its parent function using horizontal or vertical shifts, reflection, horizontal or vertical stretches and compressions with these transformation-of-linear-functions worksheets.

Train high-school students in evaluating quadratic functions, identifying the vertex, intercepts and the properties of quadratic functions and a lot more employing this printable collection of quadratic functions pdfs.

Graphing Quadratic Function Worksheets. Stacked here is a vast collection of pdf worksheets on graphing quadratic functions to identify zeros, writing the quadratic function of the parabola, identifying properties of a parabola and more.

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Transformation of Quadratic Function Worksheets. Transformation of a quadratic function and identification of various types of shifts like horizontal shift, vertical shift and reflection are the major topics discussed in this unit of high-school function worksheets.

Login Become a Member. Domain and Range Worksheets The domain and range of a function worksheets provide ample practice in determining the input and output values with exercises involving ordered pairs, tables, mapping diagrams, graphs and more.

Identifying Functions Worksheets Which of the relations are functions? Try to spot functions from ordered pairs, mapping diagrams, input-output tables, graphs and equations with this unit of pdf worksheets Function Table Worksheets These printable function table worksheets provide practice with different types of functions like linear, quadratic, polynomial, and more. Operations with Functions Worksheets Perform operations such as addition, subtraction, multiplication and division on functions with these function operations worksheets.

Evaluating Function Worksheets Get your hands on these evaluating function worksheets to practice substituting input values in different types of functions like linear, quadratic, polynomial, rational, exponential, trigonometric, and piecewise to get the output. Composition of Functions Worksheets Gain a thorough knowledge of composing two or three functions, evaluate functions and decomposing them as well with this array of printable composition of functions worksheets.

Inverse Functions Worksheets Walk through this assortment of inverse functions worksheets, examine graphs to check if two functions are inverses of each other, find the inverses of functions, and domains with restricted domains and more.Test and Worksheet Generators for Math Teachers.

All worksheets created with Infinite Algebra 2. Stop searching. Create the worksheets you need with Infinite Algebra 2.

Basics Order of operations Evaluating expressions Simplifying algebraic expressions. Linear Relations and Functions Review of linear equations Graphing absolute value functions Graphing linear inequalities. General Functions Evaluating functions Function operations Inverse functions. Equations and Inequalities Multi-step equations Work word problems Distance-rate-time word problems Mixture word problems Absolute value equations Multi-step inequalities Compound inequalities Absolute value inequalities.

Complex Numbers Operations with complex numbers Properties of complex numbers Rationalizing imaginary denominators. Radical Functions and Rational Exponents Simplifying radicals Operations with radical expressions Dividing radical expressions Radicals and rational exponents Simplifying rational exponents Square root equations Rational exponent equations Graphing radicals. Exponential and Logarithmic Functions The meaning of logarithms Properties of logarithms The change of base formula Writing logs in terms of others Logarithmic equations Inverse functions and logarithms Exponential equations not requiring logarithms Exponential equations requiring logarithms Graphing logarithms Graphing exponential functions.

Higher Education. Adult Education. Digital Resources for Students Google Apps. Internet Activities. English Language Arts. Foreign Language. Social Studies - History. History World History.

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For All Subject Areas. See All Resource Types. Transformations of Functions Worksheets.Teachers Pay Teachers is an online marketplace where teachers buy and sell original educational materials. Are you getting the free resources, updates, and special offers we send out every week in our teacher newsletter?

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### Unit 7 – Transformations of Functions

English Language Arts. Foreign Language. Social Studies - History. History World History. For All Subject Areas. See All Resource Types. In my experience, students often have a tough time grasping the concept of a "parent function" or a "family of functions".

With this visual, basic introduction to transforming linear functions, my hope is to make a memorable impression on students. A little bit of silly sometimes goes a long way. MathAlgebraAlgebra 2. Fun StuffHandoutsGraphic Organizers. Add to cart. Wish List. Task Cards: Transformations of Linear Functions. Included in this set are 32 cards containing problems over transformations of linear functions.Roundrock ISD adopted new math textbooks to be used starting with the school year.

I have kept these notes available for parents and students alike as basic algebraic fundamentals do not change. Lesson 1 Parent Functions. Parent Functions Worksheet. Lesson 2 Domain and Range. Domain and Range Worksheet. Lesson 3 Function Transformations.

Class Notes. Function Transformations Worksheet. Lesson 4 Function Notation and Function Representations.

Graphing Radical Functions & Equations, Transformations, Domain & Rangle, Plotting Points, Algebra

Function Notation and Representations Worksheet. Lesson 5 Inverse Functions. Inverse Functions Worksheet. Test Review fall Review Answers fall Lesson 1 Part 2.

Chapter 1 Rev. Lesson 2. Worksheet to accompany part 1. Lesson 6 Families of Functions. Class Notes Linear Inequalities.

Chapter 2 Rev. Review Solutions. Using Stat Plot.

Absolute Value Translations. Worksheet Assignment. Linear systems Review - 2. Linear Systems Review - covering sections from Chapters 2 and 3. Chapter 3 Rev. Lesson 5 2x2 Matrices, Determinants and Inverses.

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Solving Systems of 3 Equations :. Homework Worksheet. Lesson 4. Chapter 4 Matrix Test Review Winterbreak Tic-Tac Toe. U5 L1 Notes: Function Notation. U5 Lesson 3: Domain and Range. U5 Lesson 4: Graphing Stories. U5 Lesson 5: Intro to Sequences. Graphing Stories Practice WS if time.

Warm-up: Exponents. Notes - Exponent Rules. HW: Finish Exponent Packet. Warm-up: Exponents Review. The Perfect Rectangle. Simplify Radicals Notes. HW: Simplify Radicals Worksheet. Practice Problems. HW: none. Quick Check.

HW: Simplify Radicals Worksheet 2. HW: Arithmetic Sequences Worksheet. HW: Geometric Sequences Worksheet. Geometric Sequemces Notes. Recursive Formulas. HW: Recursive Sequences Worksheet. Extra Practice WS. Sequences Key Facts Chart.

HW: Finish extra Practice Sheet if needed. In-class review.

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Review Worksheet. HW: Sequences Review Worksheet.

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Formative Assessment - Unit 5. HW: Review Worksheet due tomorrow. M3 Lesson 11 Notes Investigation. Class Discussion. Lesson 14 - Desmos Activity. Return Tests. HW: Lesson 14 WS. Skittles Lab. Notes - Exponential Decay vs. Exponential Growth.