Deck 7: Transformations of Functions

Question 1

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

A)​
B)​
C)​
D)​
E)​

Answer 1

​

Question 2

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

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 $y = \sqrt { x } ; y = 2 - \sqrt { x }$

Answer 2

Reflection in the x-axis and vertical shift of $y = \sqrt { x } ; y = 2 - \sqrt { x }$

Question 3

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

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

Answer 3

$y = \sqrt { x } - 3$

Question 4

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

A)​
B)​
C)​
D)​
E)​

Question 5

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

A)​
B)​
C)​
D)​
E)​

Question 6

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

A)​
B)​
C)​
D)​
E)​

Question 7

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

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

Question 8

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

A) $y = | x | + 6$
B) $y = | x | - 5$
C) $y = | x | - 6$
D) $y = | x | + 7$
E) $y = | x | + 5$

Question 9

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

A)​
B)​
C)​
D)​
E)​

Question 10

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

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 11

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

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 $y = x ^ { 3 } ; y = ( x + 4 ) ^ { 3 }$

Question 12

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

A)​
B)​
C)​
D)​
E)​

Question 13

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

A) $y = - | x + 5 | - 1$
B) $y = | x + 5 | + 1$
C) $y = - | x - 5 | + 1$
D) $y = - | x - 5 | - 1$
E) $y = | x - 5 | - 1$

Question 14

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

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 $y = | x + 1 | ; y = - | x + 1 |$

Question 15

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

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 16

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

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

Question 17

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

A)Horizontal shift of the x-axis of $y = x ^ { 4 } ; y = - x ^ { 4 }$
B)Vertical shift of the y-axis of $y = x ^ { 4 } ; y = - x ^ { 4 }$
C)Reflection in the x-axis of $y = x ^ { 4 } ; y = - x ^ { 4 }$
D)Horizontal shift of the y-axis of $y = x ^ { 4 } ; y = - x ^ { 4 }$
E)Vertical shift of the x-axis of $y = x ^ { 4 } ; y = - x ^ { 4 }$

Question 18

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

A)​
B)​
C)​
D)​ ​
E)​

Question 19

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

A) $$y = ( x - 5 ) ^ { 3 } - 1$$
B) $$y = ( x + 5 ) ^ { 3 } + 2$$
C) $y = ( x + 5 ) ^ { 3 } - 2$
D) $y = ( x - 5 ) ^ { 3 } + 2$
E) $y = ( x - 5 ) ^ { 3 } + 1$

Question 20

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

A)​
B)​
C)​
D)​
E)​

Question 21

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

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 22

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.
​

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 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.
​

A)False. $| x | \neq | - x |$
B)True. $| x | = | - x |$

Question 24

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.

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 25

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

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 26

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.
​

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 27

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

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 28

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

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 29

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

A) $y = \sqrt { x } - 5$
B) $y = - \sqrt { x } + 5$
C) $y = - \sqrt { x } - 5$
D) $y = \sqrt { x } + 5$
E) $y = - \sqrt { x } - 6$

Question 30

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.

A)g(x)= [[-x]] + 8
B)g(x)= -[[x - 8]]
C)g(x)= -[[x + 8]]
D)g(x)= [[-x]] - 8
E)g(x)= -[[x]] + 8

Question 31

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

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 32

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.
​

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) $g ( x ) = ( x - 3 ) ^ { 2 } + 5$