Question 1

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

Accepted Answer

A) Horizontal shift of $y = x ^ { 3 } ; y = ( x - 4 ) ^ { 3 }$ 
B) Vertical shift of $y = x ^ { 2 } ; y = ( x - 4 ) ^ { 2 }$ 
C) Vertical shift of $y = x ^ { 2 } ; y = ( x + 4 ) ^ { 2 }$ 
D) Horizontal shift of $y = x ^ { 2 } ; y = ( x + 4 ) ^ { 2 }$ 
E) Vertical shift of $y = x ^ { 3 } ; y = ( x + 4 ) ^ { 3 }$ 
A) Horizontal shift of $y = x ^ { 3 } ; y = ( x - 4 ) ^ { 3 }$ 
B) Vertical shift of $y = x ^ { 2 } ; y = ( x - 4 ) ^ { 2 }$ 
C) Vertical shift of $y = x ^ { 2 } ; y = ( x + 4 ) ^ { 2 }$ 
D) Horizontal shift of $y = x ^ { 2 } ; y = ( x + 4 ) ^ { 2 }$ 
E) Vertical shift of $y = x ^ { 3 } ; y = ( x + 4 ) ^ { 3 }$ A

Question 2

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

Accepted Answer

A) Reflection in the x-axis of $y = | x - 1 | ; y = - | x - 1 |$ 
B) Horizontal shift of x-axis of $y = | x | ; y = | x + 1 |$ 
C) Reflection in the y-axis of $y = | x | ; y = - | x - 1 |$ 
D) Horizontal shift of x-axis of $y = | x + 1 | ; y = - | x + 1 |$ 
E) Reflection in the y-axis of $y = | x + 1 | ; y = - | x + 1 |$ 
A) Reflection in the x-axis of $y = | x - 1 | ; y = - | x - 1 |$ 
B) Horizontal shift of x-axis of $y = | x | ; y = | x + 1 |$ 
C) Reflection in the y-axis of $y = | x | ; y = - | x - 1 |$ 
D) Horizontal shift of x-axis of $y = | x + 1 | ; y = - | x + 1 |$ 
E) Reflection in the y-axis of $y = | x + 1 | ; y = - | x + 1 |$ B

Question 3

Use the given graph of f to select the graph for the following function. ​
Y = f(2x)​   ​

Accepted Answer

A) ​   
B) ​   
C) ​   
D) ​   
E) ​   
A) ​   
B) ​   
C) ​   
D) ​   
E) ​   B

Question 4

Write an equation for the function that is described by the given characteristic. ​
The shape of $f ( x ) = \sqrt { x }$ ,but shifted three units to the left and reflected in both the x-axis and the y-axis.
​

Accepted Answer

A)  $g ( x ) = \sqrt { - x + 3 }$ 
B)  $g ( x ) = - \sqrt { x + 3 }$ 
C)  $g ( x ) = - \sqrt { - x + 3 }$ 
D)  $g ( x ) = \sqrt { x + 3 }$ 
E)  $g ( x ) = - \sqrt { - x - 3 }$ 
A)  $g ( x ) = \sqrt { - x + 3 }$ 
B)  $g ( x ) = - \sqrt { x + 3 }$ 
C)  $g ( x ) = - \sqrt { - x + 3 }$ 
D)  $g ( x ) = \sqrt { x + 3 }$ 
E)  $g ( x ) = - \sqrt { - x - 3 }$

Question 5

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

Accepted Answer

A) Vertical stretch of $y = x ^ { 2 } , y = 2 x ^ { 2 }$ 
B) Horizontal stretch of $y = x ^ { 3 } ; y = 2 x ^ { 3 }$ 
C) Vertical stretch of $y = x ^ { 3 } ; y = 2 x ^ { 3 }$ 
D) Vertical stretch of $y = x ^ { 3 } ; y = - 2 x ^ { 3 }$ 
E) Horizontal stretch of $y = x ^ { 3 } ; y = - 2 x ^ { 3 }$ 
A) Vertical stretch of $y = x ^ { 2 } , y = 2 x ^ { 2 }$ 
B) Horizontal stretch of $y = x ^ { 3 } ; y = 2 x ^ { 3 }$ 
C) Vertical stretch of $y = x ^ { 3 } ; y = 2 x ^ { 3 }$ 
D) Vertical stretch of $y = x ^ { 3 } ; y = - 2 x ^ { 3 }$ 
E) Horizontal stretch of $y = x ^ { 3 } ; y = - 2 x ^ { 3 }$

Question 6

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

Accepted Answer

A)  $y = x ^ { 2 } + 3$ 
B)  $y = x ^ { 2 } + 4$ 
C)  $y = - x ^ { 2 }$ 
D)  $y = x ^ { 2 } - 3$ 
E)  $y = x ^ { 2 } - 4$ 
A)  $y = x ^ { 2 } + 3$ 
B)  $y = x ^ { 2 } + 4$ 
C)  $y = - x ^ { 2 }$ 
D)  $y = x ^ { 2 } - 3$ 
E)  $y = x ^ { 2 } - 4$

Question 7

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

Accepted Answer

A) Reflection in the x-axis and vertical shift of $y = \sqrt { x } ; y = 2 - \sqrt { x }$ 
B) Vertical shift of x-axis and vertical shift of $y = \sqrt { x } ; y = 2 + \sqrt { x }$ 
C) Reflection in the x-axis and vertical shift of $y = \sqrt { x } ; y = 2 + \sqrt { x }$ 
D) Horizontal shift of x-axis and vertical shift of $y = \sqrt { x } ; y = 2 + \sqrt { x }$ 
E) Horizontal shift of x-axis and vertical shift of $y = \sqrt { x } ; y = 2 - \sqrt { x }$ 
A) Reflection in the x-axis and vertical shift of $y = \sqrt { x } ; y = 2 - \sqrt { x }$ 
B) Vertical shift of x-axis and vertical shift of $y = \sqrt { x } ; y = 2 + \sqrt { x }$ 
C) Reflection in the x-axis and vertical shift of $y = \sqrt { x } ; y = 2 + \sqrt { x }$ 
D) Horizontal shift of x-axis and vertical shift of $y = \sqrt { x } ; y = 2 + \sqrt { x }$ 
E) Horizontal shift of x-axis and vertical shift of $y = \sqrt { x } ; y = 2 - \sqrt { x }$

Question 8

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

Accepted Answer

A)  $y = - 5 + x ^ { 3 }$ 
B)  $y = - 5 - x ^ { 3 }$ 
C)  $y = - 6 + x ^ { 3 }$ 
D)  $y = - 4 + x ^ { 3 }$ 
E)  $y = - 4 - x ^ { 3 }$ 
A)  $y = - 5 + x ^ { 3 }$ 
B)  $y = - 5 - x ^ { 3 }$ 
C)  $y = - 6 + x ^ { 3 }$ 
D)  $y = - 4 + x ^ { 3 }$ 
E)  $y = - 4 - x ^ { 3 }$

Question 9

For following function,select (on the same set of coordinate axes)a graph for $c = - 3,5 \text { and } 4$ .​ $f ( x ) = | x - c |$ ​

Accepted Answer

A) ​   
B) ​   
C) ​   
D) ​   
E) ​   
A) ​   
B) ​   
C) ​   
D) ​   
E) ​

Question 10

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

Accepted Answer

A) Reflection in the y-axis and vertical shrink of $y = \sqrt { x } ; y = \frac { 1 } { 2 } \sqrt { - x }$ . 
B) Reflection in the y-axis and vertical shrink of $y = \sqrt { - x } ; y = \frac { 1 } { 2 } \sqrt { x }$ . 
C) Reflection in the y-axis and vertical shrink of $y = \sqrt { - x } ; y = - \frac { 1 } { 2 } \sqrt { x }$ . 
D) Reflection in the y-axis and vertical shrink of $y = \sqrt { x } ; y = - \frac { 1 } { 2 } \sqrt { - x }$ . 
E) Reflection in the y-axis and vertical shrink of $y = \sqrt { x } ; y = \frac { 1 } { 2 } \sqrt { x }$ . 
A) Reflection in the y-axis and vertical shrink of $y = \sqrt { x } ; y = \frac { 1 } { 2 } \sqrt { - x }$ . 
B) Reflection in the y-axis and vertical shrink of $y = \sqrt { - x } ; y = \frac { 1 } { 2 } \sqrt { x }$ . 
C) Reflection in the y-axis and vertical shrink of $y = \sqrt { - x } ; y = - \frac { 1 } { 2 } \sqrt { x }$ . 
D) Reflection in the y-axis and vertical shrink of $y = \sqrt { x } ; y = - \frac { 1 } { 2 } \sqrt { - x }$ . 
E) Reflection in the y-axis and vertical shrink of $y = \sqrt { x } ; y = \frac { 1 } { 2 } \sqrt { x }$ .

Question 11

Use the given graph of f to select the graph for following function.​ $$y = \frac { 1 } { 2 } f ( x )$$   ​

Accepted Answer

A) ​   
B) ​   
C) ​   
D) ​   
E) ​   
A) ​   
B) ​   
C) ​   
D) ​   
E) ​

Question 12

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

Accepted Answer

A) ​ $f ( x ) = - 3 | x - 2 | + 2$ 
B)  $f ( x ) = - 3 | x + 2 | + 2$ 
C)  $f ( x ) = | - 3 x + 2 | + 2$ 
D)  $f ( x ) = - 3 | x + 2 | - 2$ 
E)  $f ( x ) = | - 3 x - 2 | + 2$ 
A) ​ $f ( x ) = - 3 | x - 2 | + 2$ 
B)  $f ( x ) = - 3 | x + 2 | + 2$ 
C)  $f ( x ) = | - 3 x + 2 | + 2$ 
D)  $f ( x ) = - 3 | x + 2 | - 2$ 
E)  $f ( x ) = | - 3 x - 2 | + 2$

Question 13

For following function,select (on the same set of coordinate axes)a graph for $c = - 1,3 \text { and } 4$ .​ $f ( x ) = | x | + c$ ​

Accepted Answer

A) ​   
B) ​   
C) ​   
D) ​   
E) ​   
A) ​   
B) ​   
C) ​   
D) ​   
E) ​

Question 14

For following function,select (on the same set of coordinate axes)a graph of function for $$c = 3,1 \text { and } - 3$$ $$f ( x ) = \left\{ \begin{array} { l } 
x ^ { 2 } + c , x < 0 \
- x ^ { 2 } + c , x \geq 0
\end{array} \right.$$ ​

Accepted Answer

A) ​   
B) ​   
C) ​   
D) ​   
E) ​   
A) ​   
B) ​   
C) ​   
D) ​   
E) ​

Question 15

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

Accepted Answer

A)  $$y = - 2 x ^ { 2 }$$ 
B)  $$y = x ^ { 2 }$$ 
C)  $y = - \frac { x ^ { 2 } } { 2 }$ 
D)  $y = \frac { x ^ { 2 } } { 2 }$ 
E)  $y = 2 x ^ { 2 }$ 
A)  $$y = - 2 x ^ { 2 }$$ 
B)  $$y = x ^ { 2 }$$ 
C)  $y = - \frac { x ^ { 2 } } { 2 }$ 
D)  $y = \frac { x ^ { 2 } } { 2 }$ 
E)  $y = 2 x ^ { 2 }$

Question 16

Write an equation for the function that is described by the given characteristic. ​
The shape of $f ( x ) = x ^ { 3 }$ ,but shifted 17 units to the right.
​

Accepted Answer

A)  $$g ( x ) = ( x + 17 )$$ 
B)  $$g ( x ) = - ( x - 17 ) ^ { 3 }$$ 
C)  $g ( x ) = ( x + 17 ) ^ { 3 }$ 
D)  $g ( x ) = ( x - 17 ) ^ { 3 }$ 
E)  $g ( x ) = - ( x + 17 ) ^ { 3 }$ 
A)  $$g ( x ) = ( x + 17 )$$ 
B)  $$g ( x ) = - ( x - 17 ) ^ { 3 }$$ 
C)  $g ( x ) = ( x + 17 ) ^ { 3 }$ 
D)  $g ( x ) = ( x - 17 ) ^ { 3 }$ 
E)  $g ( x ) = - ( x + 17 ) ^ { 3 }$

Question 17

Write an equation for the function that is described by the given characteristic. ​
The shape of $f ( x ) = x ^ { 2 }$ ,but shifted three units to the right and five units downward.
​

Accepted Answer

A)  $g ( x ) = ( x - 3 ) ^ { 2 } - 5$ 
B)  $g ( x ) = \left( x ^ { 2 } - 3 \right) - 5$ 
C)  $g ( x ) = ( x + 3 ) ^ { 2 } - 5$ 
D)  $g ( x ) = ( x + 3 ) ^ { 2 } + 5$ 
E)  $g ( x ) = ( x - 3 ) ^ { 2 } + 5$ 
A)  $g ( x ) = ( x - 3 ) ^ { 2 } - 5$ 
B)  $g ( x ) = \left( x ^ { 2 } - 3 \right) - 5$ 
C)  $g ( x ) = ( x + 3 ) ^ { 2 } - 5$ 
D)  $g ( x ) = ( x + 3 ) ^ { 2 } + 5$ 
E)  $g ( x ) = ( x - 3 ) ^ { 2 } + 5$

Question 18

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

Accepted Answer

A)  $y = 4 | x | - 4$ 
B)  $y = - 4 | x | - 4$ 
C)  $y = - 4 \| x \| - 4$ 
D)  $y = 4 | x | + 4$ 
E)  $y = - 4 | x | + 4$ 
A)  $y = 4 | x | - 4$ 
B)  $y = - 4 | x | - 4$ 
C)  $y = - 4 \| x \| - 4$ 
D)  $y = 4 | x | + 4$ 
E)  $y = - 4 | x | + 4$

Question 19

Write an equation for the function that is described by the following characteristics. The shape of $f ( x ) = x ^ { 2 }$ ,but moved five units down,four units to the left,and then reflected in the x-axis.

Accepted Answer

A)  $g ( x ) = 4 - ( x + 5 ) ^ { 2 }$ 
B)  $g ( x ) = - ( x + 4 ) ^ { 2 } - 5$ 
C)  $g ( x ) = 5 - ( x + 4 ) ^ { 2 }$ 
D)  $g ( x ) = - ( x + 5 ) ^ { 2 } - 4$ 
E)  $g ( x ) = 5 - ( x - 4 ) ^ { 2 }$ 
A)  $g ( x ) = 4 - ( x + 5 ) ^ { 2 }$ 
B)  $g ( x ) = - ( x + 4 ) ^ { 2 } - 5$ 
C)  $g ( x ) = 5 - ( x + 4 ) ^ { 2 }$ 
D)  $g ( x ) = - ( x + 5 ) ^ { 2 } - 4$ 
E)  $g ( x ) = 5 - ( x - 4 ) ^ { 2 }$

Question 20

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

Accepted Answer

A) ​ $y = \sqrt { x } + 5$ 
B)  $y = - \sqrt { x - 5 } + 5$ 
C)  $y = \sqrt { x + 5 } + 5$ 
D)  $y = - \sqrt { x } - 5$ 
E) None of the above 
A) ​ $y = \sqrt { x } + 5$ 
B)  $y = - \sqrt { x - 5 } + 5$ 
C)  $y = \sqrt { x + 5 } + 5$ 
D)  $y = - \sqrt { x } - 5$ 
E) None of the above

Exam 7: Transformations of Functions

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

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

Use the given graph of f to select the graph for the following function. ​ Y = f(2x)​ ​

Write an equation for the function that is described by the given characteristic. ​ The shape of f(x)=xf ( x ) = \sqrt { x }f(x)=x​ ,but shifted three units to the left and reflected in both the x-axis and the y-axis. ​

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

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

For following function,select (on the same set of coordinate axes)a graph for c=−3,5 and 4c = - 3,5 \text { and } 4c=−3,5 and 4 .​ f(x)=∣x−c∣f ( x ) = | x - c |f(x)=∣x−c∣ ​

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

Use the given graph of f to select the graph for following function.​ y=12f(x)y = \frac { 1 } { 2 } f ( x )y=21​f(x) ​

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

For following function,select (on the same set of coordinate axes)a graph for c=−1,3 and 4c = - 1,3 \text { and } 4c=−1,3 and 4 .​ f(x)=∣x∣+cf ( x ) = | x | + cf(x)=∣x∣+c ​

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

Write an equation for the function that is described by the given characteristic. ​ The shape of f(x)=x3f ( x ) = x ^ { 3 }f(x)=x3 ,but shifted 17 units to the right. ​

Write an equation for the function that is described by the given characteristic. ​ The shape of f(x)=x2f ( x ) = x ^ { 2 }f(x)=x2 ,but shifted three units to the right and five units downward. ​

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

Write an equation for the function that is described by the following characteristics. The shape of f(x)=x2f ( x ) = x ^ { 2 }f(x)=x2 ,but moved five units down,four units to the left,and then reflected in the x-axis.

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

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

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

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

Use the given graph of f to select the graph for the following function. Y = f(2x)

Write an equation for the function that is described by the given characteristic. The shape of $f ( x ) = \sqrt { x }$ ,but shifted three units to the left and reflected in both the x-axis and the y-axis.

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 $f ( x ) = x ^ { 2 }$ 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. $

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 $f ( x ) = x ^ { 3 }$ 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. $

For following function,select (on the same set of coordinate axes)a graph for $c = - 3,5 \text { and } 4$ . $f ( x ) = | x - c |$

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

Use the given graph of f to select the graph for following function. $y = \frac { 1 } { 2 } f ( x )$ $Use the given graph of f to select the graph for following function. y = \frac { 1 } { 2 } f ( x ) $

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

For following function,select (on the same set of coordinate axes)a graph for $c = - 1,3 \text { and } 4$ . $f ( x ) = | x | + c$

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. $

Write an equation for the function that is described by the given characteristic. The shape of $f ( x ) = x ^ { 3 }$ ,but shifted 17 units to the right.

Write an equation for the function that is described by the given characteristic. The shape of $f ( x ) = x ^ { 2 }$ ,but shifted three units to the right and five units downward.

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

Write an equation for the function that is described by the following characteristics. The shape of $f ( x ) = x ^ { 2 }$ ,but moved five units down,four units to the left,and then reflected in the x-axis.

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. $