Free Printable Families of Functions Translations

1.

Given the function $y=\left(x+4\right)^2+2$ , what is the parent function?

a)

$y=x^2$

b)

$y=a\left(x-h\right)^2+k$

c)

$y=mx+b$

d)

$y=0\left(x-0\right)^2+0$

2.

$y=\sqrt{x-\frac{3}{2}}+2$ belongs to what family of functions?

a)

square root

b)

absolute value

c)

linear

d)

quadratic

3.

Write the equation that results if the parent absolute value function is shifted right 15 units, down 3 units, and reflected vertically.

a)

$y=-\left|x-15\right|-3$

b)

$y=-\left|x+15\right|-3$

c)

$y=\frac{1}{2}\left|x+3\right|-15$

d)

$y=\frac{1}{2}\left|x-3\right|-15$

e)

$y=\left|-x-15\right|-3$

4.

Which transformations are involved in the equation $y=\frac{1}{2}\left|x\ +\ 1\right|-1$ ?

a)

Horizontal translation left

b)

Vertical shrink

c)

Vertical translation down

d)

Horizontal translation right

e)

Vertical stretch

5.

If $f\left(x\right)=a\left(x-h\right)^2+k$ has a horiz. shift of -2, a vertical shift of +3 and a vertical stretch of 4, what are the values of a, h, and k?

a)

$a=4;\ h=-2;\ k=3$

b)

$a=2;\ h=4;\ k=-3$

c)

$a=4;\ h=2;\ k=3$

d)

$a=3;\ h=2;\ k=-4$

6.

If $f\left(x\right)=a\left(x-h\right)^2+k$ has a horiz. shift of -2, a vert. shift of 3 and a vert. stretch of 4, what is the equation for $f\left(x\right)$ ?

a)

$f\left(x\right)=4\left(x+2\right)^2+3$

b)

$f\left(x\right)=4\left(x-2\right)^2+3$

c)

$f\left(x\right)=3\left(x+2\right)^2+4$

d)

$f\left(x\right)=2\left(x-4\right)^2+3$

7.

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

8.

What does the transformation $f\left(x\right)\ \rightarrow\ \frac{1}{3}f\left(x\right)+4$ do to the graph of $f\left(x\right)$ ?

a)

Shrinks the graph vertically by a factor of 1/3 and translates up 4 units.

b)

Stretches the graph by a factor of 3 and translates up 4 units.

c)

Translates the graph left 1/3 of a unit and up 4 units.

d)

Translates the graph right 3 unites and down 4 units.

9.

Which of the following are contained in the pictured graph

a)

A minimum

b)

a maximum

c)

a quadratic function

d)

an absolute value function

e)

a y-intercept at 0.

10.

What is the equation of the graph below?

a)

f(x ) = I x + 4 I + 2

b)

f(x ) = -I x - 4 I + 2

c)

f(x ) = I x - 4 I + 2

d)

f(x ) = -I x + 4 I + 2

11.

What is the equation of the graph below?

a)

f(x) = - I x + 2 I

b)

f(x) = - I x - 2 I

c)

f(x) = I x + 2 I

d)

f(x) = I x - 2 I

12.

What is the equation of the graph below?

a)

f(x) = I x I -1

b)

f(x) = I x I +1

c)

f(x) = - I x I -1

d)

f(x) = -I x I +1

13.

What is the equation of the graph below?

a)

f(x) = I x + 2 I

b)

f(x) = I x + 2 I +2

c)

f(x) = I x - 2 I +2

d)

f(x) = I x - 2 I

14.

Describe the transformation of the equation below from the parent function of y = I x I
y = -2 I x - 3 I + 3

a)

reflected over x axis, stretched by 2, right 3, up 3

b)

reflected over x axis, stretched by 2, left 3 up 3.

c)

reflected over x axis, shrunk by 2, right 3, up 3

d)

reflected over the x axis, shrunk by 2, left 3, up 3

15.

What is the equation of the absolute value function?

a)

f(x)= 4|x+3|

b)

f(x)= 1/4 |x+3|

c)

f(x)= 1/4 |x - 3|

d)

f(x)= 4|x - 3|

16.

What is the domain of the absolute value function?

a)

(4, 0)

b)

(0, 4)

c)

(-infinity, infinity)

d)

[4, infinity)

17.

Describe the transformations from the parent graph to f(x) = -3∣x + 5∣ - 7

a)

Down 7, Left 5, Stretch by 3, Flip

b)

Up 7, Right 5, Stretch by 3, Flip

c)

Down 7, Left 5, Compress by 3, Flip

d)

Up 7, Right 5, Compress by 3, Flip

18.

What is the range of the absolute value function?

a)

(-infinity, infinity)

b)

[3, infinity)

c)

[0, infinity)

d)

(-infinity, 3]

19.

Write the equation for a graph that is vertically compressed by a factor of 2/5 and shifted right 6.

a)

y=6|x|-2/5

b)

y=2/5|x|+6

c)

y=2/5|x+6|

d)

y=2/5|x-6|

20.

Describe the transformation of y = x² + 4

a)

Shift UP

b)

Shift DOWN

c)

Shift LEFT

d)

Shift RIGHT

21.

Describe the transformation of y = (x - 4)²

a)

Shift UP

b)

Shift DOWN

c)

Shift LEFT

d)

Shift RIGHT

22.

Compare the function y = 0.3x² to the parent function y = x²

a)

Wider

b)

Narrower

23.

Compare the function y = 5x² to the parent function y = x²

a)

Wider

b)

Narrower

24.

How did we transform from the parent function?
y = x² + 2

a)

horizontal shift up

b)

vertical shift up

c)

horizontal shift down

d)

vertical shift down

25.

Match the equation to its description.

a)

Reflected over x and stretched by 3

b)

Stretched by 3

c)

Reflected over x

d)

Reflected over x and up 3

26.

Match the equation to its description.

a)

Stretched by 4 and up 4

b)

Compressed by 4 and up 4

c)

Stretched by 4 and left 4

d)

Compressed by 4 and left 4

27.

Match the equation to its description.

a)

Reflected over x, right 2 and up 1

b)

Reflected over x, left 2 and up 1

c)

Reflected over x, right 2 and down 1

d)

Reflected over x, left 2 and down 1

28.

If the blue is f(x)=x^2,then the red must be

a)

g(x)=x²-5

b)

g(x)=x²+5

c)

g(x)=(x-5)²

d)

g(x)=(x+5)²

29.

If the blue is f(x)=x^2,the red must be

a)

g(x)=(x+3)²

b)

g(x)=(x-3)²

c)

g(x)=x²+3

d)

g(x)=x²-2

30.

Describe the transformation of y = 3(x - 3)² + 3

a)

Narrow, Right, Up

b)

Narrow, Left, Down

c)

Wide, Right, Up

d)

Wide, Left, Down

31.

Which of the following is the correct equation for the given graph?

a)

f(x) = -(x + 2)² - 4

b)

f(x) = -(x - 2)² - 4

c)

f(x) = -3(x - 2)² - 4

d)

f(x) = -3(x + 2)² - 4

32.

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

33.

If red represents y = x², which equation represents black?

a)

y = 7x²

b)

y = -7x²

c)

y = -(1/7)x²

d)

y = -5x²

34.

In what Disney film do you find a group of vegetarian sharks?

a)

Toy Story

b)

Mulan

c)

Finding Nemo

d)

Sleeping Beauty

35.

Who is this?

a)

Pumba

b)

Timon

c)

Simba

d)

Troy

36.

What is his song?

a)

Under the Sea

b)

Hakuna Matata

c)

Colors of the Wind

d)

Strangers Like Me

37.

Who did sing the song "I would like?"

a)

Zara Larson

b)

Madonna

c)

Katy Perry

d)

Taylor Swift

38.

How many members of One Direction are there?

a)

5

b)

4

c)

6

d)

3

39.

Which one of these artists recently beat Adele's record sales?

a)

Justin beiber

b)

Justin Timberlake

c)

Bruno Mars

d)

Ed Sheeran

40.

Finally, who wrote the album "1989"?

a)

Katy Perry

b)

Lourde

c)

Brittany Spears

d)

Taylor Swift

41.

Which parent function matches the graph?

a)

y = |x|

b)

y = x

c)

y = x²

d)

y = 2^x

42.

What type of function is shown?

a)

absolute value

b)

quadratic

c)

linear

d)

exponential

43.

Name the parent function.

a)

constant

b)

square root

c)

linear

d)

absolute value

44.

Which equation below is a quadratic function translated up 5 units?

a)

y = x² + 5

b)

y = (x + 5)²

c)

y = 5x²

d)

y = -x² - 5

45.

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

46.

Which equation is a quadratic function reflected over the x-axis and shifted up 2.

a)

y = x² + 2

b)

y = -x² + 2

c)

y = x² - 2

d)

y = -(x + 2)²

47.

Which equation is a quadratic function reflected over the x-axis and shifted up 2.

a)

y = x² + 2

b)

y = -x² + 2

c)

y = x² - 2

d)

y = -(x + 2)²

48.

Tell how the graph transformed.
y = (x - 3)²

a)

Translated right 3

b)

Translated left 3

c)

Translated up 3

d)

Translated down 9

49.

a)

Left 2; Up 2

b)

Right 2; Down 2

c)

Left 2; Up 2; Reflection over x-axis

d)

Vertical stretch by factor of 3; Right 2; Down 2

50.

a)

Left 2, Down 2, Vertical Stretch

b)

Right 2; Up 1;

c)

Vertical Stretch; Right 2; Up 1

d)

Left 2; Down 2;

51.

a)

Absolute Value

b)

Quadratic

c)

Cubic

d)

Linear

52.

a)

f(x)=3∣x−2∣−2

b)

f(x)=1/3∣x+2∣−2

c)

f(x)=3∣x+2∣−2

d)

f(x) = 1/3∣x−2∣+2

Families of Functions Translations

Total questions: 52

Worksheet time: 4hrs 42mins

Similar Resources on Wayground