Exam 7: Transformations of Functions

Use the graph of $f ( x ) = x ^ { 2 }$ to write an equation for the function whose graph is shown. $Use the graph of f ( x ) = x ^ { 2 } to write an equation for the function whose graph is shown. $

(Multiple Choice)

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Question 21

Use the graph of $f ( x ) = | x |$ to write an equation for the function whose graph is shown.

(Multiple Choice)

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Question 22

Use the graph of $f ( x ) = x ^ { 3 }$ to write an equation for the function whose graph is shown. $Use the graph of f ( x ) = x ^ { 3 } to write an equation for the function whose graph is shown. $

(Multiple Choice)

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Question 23

Determine whether the statement is true or false.Justify your answer. The graphs of $f ( x ) = | x | + 5$ and $f ( x ) = | - x | + 5$ are identical.

(Multiple Choice)

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Question 24

Identify the parent function and the transformation shown in the graph.Write an equation for the function shown in the graph.

(Multiple Choice)

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Question 25

Use the graph of $f ( x ) = \sqrt { x }$ to write an equation for the function whose graph is shown. $Use the graph of f ( x ) = \sqrt { x } to write an equation for the function whose graph is shown. $

(Multiple Choice)

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Question 26

Use the graph of $f ( x ) = | x |$ to write an equation for the function whose graph is shown.

(Multiple Choice)

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Question 27

Use the viewing window shown to select a possible equation for the transformation of the parent function.

(Multiple Choice)

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Question 28

Write an equation for the function that is described by the following characteristics. The shape of f(x)= [[x]],but reflected in the y-axis,moved eight units down.

(Multiple Choice)

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Question 29

For following function,select (on the same set of coordinate axes)a graph for $c = - 3 , - 5 \text { and } - 1$ . $f ( x ) = \sqrt { x + c }$

(Multiple Choice)

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Question 30

Use the given graph of f to select the graph for following function. $y = f ( x + 1 )$

(Multiple Choice)

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Question 31

Use the given graph of f to select the graph for the following function. $y = f ( - x )$

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Question 32

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Exam 7: Transformations of Functions

Use the graph of f(x)=x2f ( x ) = x ^ { 2 }f(x)=x2 to write an equation for the function whose graph is shown. ​​ ​

Use the graph of f(x)=∣x∣f ( x ) = | x |f(x)=∣x∣ to write an equation for the function whose graph is shown.​ ​

Use the graph of f(x)=x3f ( x ) = x ^ { 3 }f(x)=x3 to write an equation for the function whose graph is shown. ​​ ​

Determine whether the statement is true or false.Justify your answer. ​ The graphs of f(x)=∣x∣+5f ( x ) = | x | + 5f(x)=∣x∣+5 and f(x)=∣−x∣+5f ( x ) = | - x | + 5f(x)=∣−x∣+5 are identical. ​

Identify the parent function and the transformation shown in the graph.Write an equation for the function shown in the graph.​ ​

Use the graph of f(x)=xf ( x ) = \sqrt { x }f(x)=x​ to write an equation for the function whose graph is shown. ​​ ​

Use the graph of f(x)=∣x∣f ( x ) = | x |f(x)=∣x∣ to write an equation for the function whose graph is shown. ​​ ​

Use the viewing window shown to select a possible equation for the transformation of the parent function.​ ​

Write an equation for the function that is described by the following characteristics. The shape of f(x)= [[x]],but reflected in the y-axis,moved eight units down.

For following function,select (on the same set of coordinate axes)a graph for c=−3,−5 and −1c = - 3 , - 5 \text { and } - 1c=−3,−5 and −1 .​ f(x)=x+cf ( x ) = \sqrt { x + c }f(x)=x+c​ ​

Use the given graph of f to select the graph for following function.​ y=f(x+1)y = f ( x + 1 )y=f(x+1) ​​ ​

Use the given graph of f to select the graph for the following function.​ y=f(−x)y = f ( - x )y=f(−x) ​ ​

Rectangular Coordinates

Graphs of Equations

Linear Equations in Two Variables

Functions

Analyzing Graphs of Functions

A Library of Parent Functions

Combinations of Functions Composite Functions

Inverse Functions

Mathematical Modeling and Variation

Quadratic Functions and Models

Polynomial Functions of Higher Degree

Polynomial and Synthetic Division

Complex Numbers

Zeros of Polynomial Functions

Rational Functions

Nonlinear Inequalities

Exponential Functions and Their Graphs

Logarithmic Functions and Their Graphs

Properties of Logarithms

Exponential and Logarithmic Equations

Exponential and Logarithmic Models

Radian and Degree Measure

Trigonometric Functions The Unit Circle

Right Triangle Trigonometry

Trigonometric Functions of Any Angle

Graphs of Sine and Cosine Functions

Graphs of Other Trigonometric Functions

Inverse Trigonometric Functions

Applications and Models

Using Fundamental Identities

Verifying Trigonometric Equations

Solving Trigonometric Equations

Sum and Difference Formulas

Multiple Angle and Product to Sum Formulas

Law of Sines

Law of Cosines

Vectors in the Plane

Vectors and Dot Products

Trigonometric Form of a Complex Number

Linear and Nonlinear Systems of Equations

Two Variable Linear Systems

Multivariable Linear Systems

Partial Fractions

Systems of Inequalities

Linear Programming

Matrices and Systems of Equations

Operations With Matrices

The Inverse of a Square Matrix

The Determinant of a Square Matrix

Applications of Matrices and Determinants

Sequences and Series

Arithmetic Sequences and Partial Sums

Geometric Sequences and Series

Mathematical Induction

The Binomial Theorem

Counting Principles

Probability

Lines

Introduction to Conics Parabolas

Ellipses

Hyperbolas

Rotation of Conics

Parametric Equations

Polar Coordinates

Polar Equations of Conics

Graphs of Polar Equations

Filters

Use the graph of $f ( x ) = x ^ { 2 }$ to write an equation for the function whose graph is shown. $Use the graph of f ( x ) = x ^ { 2 } to write an equation for the function whose graph is shown. $

Use the graph of $f ( x ) = | x |$ to write an equation for the function whose graph is shown.

Use the graph of $f ( x ) = x ^ { 3 }$ to write an equation for the function whose graph is shown. $Use the graph of f ( x ) = x ^ { 3 } to write an equation for the function whose graph is shown. $

Determine whether the statement is true or false.Justify your answer. The graphs of $f ( x ) = | x | + 5$ and $f ( x ) = | - x | + 5$ are identical.

Identify the parent function and the transformation shown in the graph.Write an equation for the function shown in the graph.

Use the graph of $f ( x ) = \sqrt { x }$ to write an equation for the function whose graph is shown. $Use the graph of f ( x ) = \sqrt { x } to write an equation for the function whose graph is shown. $

Use the graph of $f ( x ) = | x |$ to write an equation for the function whose graph is shown.

Use the viewing window shown to select a possible equation for the transformation of the parent function.

For following function,select (on the same set of coordinate axes)a graph for $c = - 3 , - 5 \text { and } - 1$ . $f ( x ) = \sqrt { x + c }$

Use the given graph of f to select the graph for following function. $y = f ( x + 1 )$

Use the given graph of f to select the graph for the following function. $y = f ( - x )$