Free Printable Translations of Functions

1.

What equation represents the quadratic function?

a)

y = (x - 4)²

b)

y = (x + 4)²

c)

y = x² - 4

d)

y = x² + 4

2.

TRUE OR FALSE:

The vertex of the function (-4, 0) is also the x-intercept.

a)

false

b)

true

3.

What equation represents the quadratic function?

a)

y = (x - 8)²

b)

y = (x + 8)²

c)

y = x² - 8

d)

y = x² + 8

4.

What equation represents the quadratic function?

a)

y = (x - 7)² - 2

b)

y = (x + 7)² + 2

c)

y = (x + 7)² - 2

d)

y = (x + 2)² + 7

5.

What equation represents the quadratic function?

a)

y = (x - 5)² - 3

b)

y = (x - 5)² + 3

c)

y = (x + 5)² - 3

d)

y = (x - 3)² - 5

6.

Which equation below is a quadratic function translated left 4 units?

a)

y = x² + 4

b)

y = (x + 4)²

c)

y = (x - 4)²

d)

y = 4x²

7.

What kind of shift is represented?

a)

up 1 unit

b)

left 1 unit

c)

right 1 unit

d)

down 1 unit

8.

Where is the y-intercept of this function?

a)

(0, 1)

b)

(0, 4)

c)

(0, -3)

d)

(0, -4)

e)

this function does not have a y-intercept

9.

What does the transformation $f\left(x\right)\ \rightarrow\ f\left(x+1\right)-9$ do to the graph of $f\left(x\right)$ ?

a)

translates it left one unit and down 9 units

b)

translates it right one unit and down 9 units

c)

translates it up one unit and right 9 units

d)

translates it down one unit and left 9 units

10.

What type of function is shown?

a)

exponential

b)

logarithm

c)

quadratic

d)

square root

11.

Which parent function matches the graph?

a)

f(x) = x

b)

f(x)= x²

c)

f(x) = |x|

d)

f(x) = ab^x

12.

Which parent function matches the graph?

a)

f(x) = x

b)

f(x) = x²

c)

f(x) =2^x

d)

f(x) =|x|

13.

Name the parent function.

a)

quadratic

b)

exponential

c)

linear

d)

absolute value

14.

Name the parent function.

a)

linear

b)

quadratic

c)

absolute value

d)

exponential

15.

What is the range of this graph?

(the x and y axis intervals are 1 unit per box)

a)

$y\ge-\frac{1}{2}$

b)

$y>-3$

c)

$y\ge-3$

d)

y exists in all real numbers

16.

What is the vertex of the absolute value function?

a)

(4, 0)

b)

(0, 4)

c)

it doesn't have one

d)

all real numbers

17.

Select all true statements about the function.

a)

$y\ge4\$ is the range of this function.

b)

The domain of the function is x exists in all real numbers.

c)

f(x)= |x| + 4 is the equation of the function.

d)

This function shows a vertical translation from the parent.

18.

y = |x| - 7 makes the graph slide . . .

a)

left 7

b)

right 7

c)

up 7

d)

down 7

19.

If $f\left(x\right)=x^{100}$ is moved 10 spaces right and 11 spaces down, what is the equation of the function?

a)

$g\left(x\right)=\left(x-11\right)^{100}-10$

b)

$g\left(x\right)=\left(x+10\right)^{100}-11$

c)

$g\left(x\right)=\left(x-10\right)^{100}-11$

d)

$g\left(x\right)=\left(x+11\right)^{100}-10$

20.

What is the y-intercept of g(x)?

f(x) = 2x -----> g(x) = 2x + 4

a)

(0, 0)

b)

(0, 4)

c)

(4, 0)

d)

(0, -4)

21.

Describe the transformation of the graph f(x) = 2^x ----> g(x) = (2)^x + 6

a)

Right 6

b)

Left 6

c)

Up 6

d)

Down 6

22.

Which equation would represent a move of 2 units up for parent function f(x) = 7x

a)

g(x) = 9x

b)

g(x) = 7x + 2

c)

g(x) = 7(x+2)

d)

g(x) = 7(x-2)

23.

What transformations have happened to f(x) = 2^x if the new equation is g(x) = 2^(x+3) -6

a)

It stayed the same

b)

up 3, left 6

c)

right 3, down 6

d)

left 3, down 6

24.

Where is the vertex of g(x)?

f(x) = x²

g(x) = (x + 4)²

a)

(0, 4)

b)

(4, 0)

c)

(-4, 0)

d)

(0, -4)

25.

The function rule for vertical shifts is _________________.

a)

$f\left(x\right)\ +\ k$

b)

$f\left(x\ +\ k\right)$

26.

a)

Yes, "+3" on the end of the function moves the function to the right 3 units

b)

No, "+3" on the end of the function moves the function to the left 3 units

c)

No, "+3" on the end of the function moves the function to the down 3 units

d)

No, "+3" on the end of the function moves the function to the up 3 units

27.

Select all the equations that show a vertical shift from its parent function.

a)

$y=\left|x+1\right|$

b)

$y=2^x+4$

c)

$y=x-10$

d)

$y=\left(x-3\right)^2$

e)

$y=x^2-1$

28.

Select all equations that show a horizontal shift from its parent function.

a)

$y=\left|x-4\right|$

b)

$y=2^{\left(x-9\right)}$

c)

$y=x^2+8$

d)

$y=\left|x\right|-5$

e)

$y=2^x+1$

29.

Select all functions that have a domain that exists in all real numbers.

a)

$y=2x-5$

b)

$y=x^2-1$

c)

$y=5^x-6$

d)

$y=\left|x+10\right|$

e)

$y=\left(x-4\right)^2$

30.

Select the equations that have an absolute minimum.

a)

$y=x^2-8$

b)

$y=2x+6$

c)

$y=2^x-3$

d)

$y=\left|x-5\right|$

31.

Select any of the functions that have a vertex at (-7, 2).

a)

$f\left(x\right)\ =\ \left(x+7\right)^2-2$

b)

$f\left(x\right)\ =\ \left|x-2\right|+7$

c)

$f\left(x\right)\ =\ \left(x+7\right)^2+2$

d)

$f\left(x\right)\ =\ \left|x-7\right|-2$

e)

$f\left(x\right)=\left|x+2\right|+7$

32.

What is the equation of the asymptote?

$f\left(x\right)\ =\ 2^x+7$

a)

y = 7

b)

y = 2

c)

y = 0

d)

y = 5

33.

What is the equation of the asymptote?

$f\left(x\right)\ =\ 2^{\left(x+1\right)}-10$

a)

y = 9

b)

y = -9

c)

y = -10

d)

y = -1

e)

y = 0

34.

What is the domain of the function?

$f\left(x\right)\ =\ \left|x+3\right|-2$

a)

x exists in all real numbers

b)

$x\ge3$

c)

$x\le-3$

d)

$x<-2$

35.

What is the vertex of a quadratic shifted 5 units right and 2 units down?

a)

(5, -2)

b)

(2, -5)

c)

(-5, 2)

d)

(-2, 5)

36.

What is the equation of this graph?

a)

f(x) = (x -5)² + 1

b)

f(x) = (x - 1)² - 5

c)

f(x) = (x + 1)² - 5

d)

f(x) = (x + 5)² +1

37.

What is the range of the function?

a)

$y\le4$

b)

$y\le0$

c)

$y\ge4$

d)

$y\ge1$

38.

What is the equation of the horizontal asymptote?

a)

y=1

b)

y=0

39.

Select all the true statements about the function.

a)

This function shows a vertical shift from the parent.

b)

This function shows a horizontal shift from the parent.

c)

The asymptote of this function is the same as the asymptote of the parent function.

d)

$y>0$ is the range of this function.

e)

$y\ >-1$ is the range of this function.

40.

Given y=4^(x+1)determine the y-intercept

a)

(0,1)

b)

(0,4)

41.

Select the parent function(s) that pass through the origin.

a)

linear

b)

quadratic

c)

absolute value

d)

exponential

42.

Select the parent functions that exist only in Quadrants 1 and 2.

a)

linear

b)

absolute value

c)

quadratic

d)

exponential

43.

Assume the functions $f\left(x\right)\ =\ 2^x-3\ \ \ \ \ \ and\ \ \ \ \ \ g\left(x\right)\ =\ 2^x+14$ are graphed together on a coordinate plane. How many spaces away vertically are the asymptotes of both functions?

a)

17 units away

b)

14 units away

c)

11 units away

44.

The function rule for horizontal shifts is _________________.

a)

$f\left(x\right)+k$

b)

$f\left(x\ +\ k\right)$

45.

The vertex of a quadratic function is (-1, 1). What is the equation of the function?

a)

$f\left(x\right)\ =\ \left(x-1\right)^2-1$

b)

$f\left(x\right)\ =\ \left(x+1\right)^2+1$

c)

$f\left(x\right)\ =\ \left(x+1\right)^2-1$

d)

$f\left(x\right)\ =\ \left(x\right)^2+1$

Translations of Functions

Total questions: 45

Worksheet time: 1hrs 1mins

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