Free Printable Transformations of Parent Functions (Abs. Value/Quadratic)

1.

Describe the transformation from the parent absolute value function:

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

a)

Shift up 5 units

b)

Shift down 5 units

c)

Shift right 5 units

d)

Shift left 5 units

2.

Describe the transformation from the parent absolute value function:

$y=8\left|x\right|$

a)

Vertical stretch by a factor of 8

b)

Vertical shrink by a factor of 8

3.

Describe the transformation from the parent quadratic function:

$y=\frac{1}{4}x^2$

a)

Vertical stretch by a factor of ¼

b)

Vertical shrink by a factor of ¼

4.

Describe the transformation from the parent absolute value function:

$y=-\left|x+4\right|-3$

* Select THREE answers *

a)

Reflection over the x-axis

b)

Translation 4 units left

c)

Translation 4 units up

d)

Translation 3 units left

e)

Translation 3 units down

5.

Describe the transformation

a)

left 2 up 5

b)

right 2 up 5

c)

left 2 down 5

d)

right 2 down 5

6.

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

7.

Tell how the function transformed from y =|x|
y = -2|x|

a)

Translated left 2 units

b)

Reflected over x-axis

c)

Stretched vertically and reflected over x-axis

d)

Compressed vertically and reflected over the x-axis

8.

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)

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

9.

Describe the transformation(s) in the following function.

$f\left(x\right)=\frac{4}{5}\left|x+5\right|+2$

a)

Vertical stretch by a factor of $\frac{4}{5}$ ,

Shift left 5 units,

Shift down 2 units

b)

Vertical compression by a factor of $\frac{4}{5}$ ,

Shift right 5 units,

Shift up 2 units

c)

Vertical stretch by a factor of $\frac{4}{5}$ ,

Shift right 5 units,

Shift up 2 units

d)

Vertical compression by a factor of $\frac{4}{5}$ ,

Shift left 5 units,

Shift up 2 units

e)

Vertical compression by a factor of $\frac{4}{5}$ ,

Shift left 5 units,

Shift down 2 units

10.

Describe the transformation from the parent graph

a)

Reflect over x, right 3, down 4

b)

Reflect over y, right 3, down 4

c)

Reflect over x, right 3, up 4

d)

Reflect over y, left 3, down 4

11.

Match the equation with the graph:

a)

y = (x - 2)² + 4

b)

y = -(x - 4)² + 2

c)

y = -(x - 2)² + 4

d)

y = -(x + 2)² + 4

12.

Which parent function matches the graph?

a)

$y=1$

b)

$y=x$

c)

$y=\left|x\right|$

d)

$y=x^2$

13.

Describe the transformation that is applied to the parent function. $f(x)=\left|x\right|-5$

a)

Shifts left 5

b)

Shifts right 5

c)

Shifts up 5

d)

Shifts down 5

14.

What shifts have occurred?

a)

left 1, up 5

b)

left 1, down 5

c)

right 1, down 5

d)

right 1, up 5

15.

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)

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

16.

Describe the transformation of the equation below from the absolute value parent function $y=-2\left|x-3\right|+3$

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

17.

Describe the transformation that is applied to the parent function.

$f(x)=3\left|x+8\right|$

a)

Stretches by 3, Shifts left 8

b)

Stretches by 3, Shifts right 8

c)

Stretches by 3, Shifts up 8

d)

Stretches by 3, Shifts down 8

18.

Describe the transformation that is applied to the parent function. $f(x)=\frac{1}{2}\left|x-1\right|-1$

a)

Shrinks by (1/2), Shifts left 1, down 1

b)

Shrinks by (1/2), Shifts right 1, down 1

c)

Shrinks by (1/2), Shifts left 1, up 1

d)

Shrinks by (1/2), Shifts right 1, up 1

19.

What is the equation to this graph?

a)

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

b)

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

c)

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

d)

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

20.

Describe the transformation(s) in the following function.

$f\left(x\right)=\frac{4}{5}\left|x+5\right|+2$

a)

Vertical stretch by a factor of $\frac{4}{5}$ ,

Shift left 5 units,

Shift down 2 units

b)

Vertical shrink by a factor of $\frac{4}{5}$ ,

Shift right 5 units,

Shift up 2 units

c)

Vertical stretch by a factor of $\frac{4}{5}$ ,

Shift right 5 units,

Shift up 2 units

d)

Vertical shrink by a factor of $\frac{4}{5}$ ,

Shift left 5 units,

Shift up 2 units

e)

Vertical shrink by a factor of $\frac{4}{5}$ ,

Shift left 5 units,

Shift down 2 units

21.

Which of the following graphs is the parent function to the function

$f\left(x\right)=2\left|x-2\right|+6$ ?

a)

b)

c)

d)

22.

a)

$y=\left|x+2\right|-1$

b)

$y=-\left|x+2\right|-1$

c)

$y=-\left|x-2\right|-1$

d)

$y=-\left|x+1\right|-2$

23.

What type of function is shown?

a)

absolute value

b)

quadratic

c)

linear

d)

exponential

24.

Name the parent function.

a)

linear

b)

quadratic

c)

absolute value

d)

constant

25.

Which parent function matches the graph?

a)

$y=|x|$

b)

$y=x$

c)

$y=x^2$

d)

$y=2^x$

26.

Which equation is an absolute value graph shifted right 5 units?

a)

$y=|x-5|$

b)

$y=|x+5|$

c)

$y=|x|+5$

d)

$y=-5|x|$

27.

The absolute value of a negative number is a positive number?

a)

True

b)

False

28.

What is the reason that absolute value is always written as a positive?

a)

Absolute value is talking about numbers so it must be positive.

b)

Absolute value does not always have to be positive.

c)

Absolute value is like a clock it has only positive numbers.

d)

Absolute value is talking about distance, distance is always measured by positive numbers.

29.

What is the vertex of the following Absolute Value graph?

a)

y = 0

b)

(0,0)

c)

x=0

d)

(-1,0)

30.

What is the domain of the following graph?

a)

$\left(-\infty,\infty\right)$

b)

$\left[0,\infty\right]$

c)

$\left(-\infty,0\right]$

d)

[0,0]

31.

Use Narrow, wide, or same to compare the width of this graph to the parent function.
y=4|x+3|-2

a)

Narrow

b)

Wide

c)

Same

32.

What is the vertex of the absolute value function?

a)

(4, 0)

b)

(0, 4)

c)

(-infinity, infinity)

d)

[4, infinity)

33.

What is the new equation?

a)

$g\left(x\right)=4\left|x\right|$

b)

$g\left(x\right)=-4\left|x\right|$

c)

$g\left(x\right)=\frac{1}{4}\left|x\right|$

d)

$g\left(x\right)=-\frac{1}{4}\left|x\right|$

34.

What is the new equation?

a)

$g\left(x\right)=-\frac{4}{3}\left|x\right|$

b)

$g\left(x\right)=\frac{4}{3}\left|x\right|$

c)

$g\left(x\right)=-\frac{3}{4}\left|x\right|$

d)

$g\left(x\right)=\frac{3}{4}\left|x\right|$

35.

What is the new equation?

a)

$g\left(x\right)=-\frac{3}{2}\left|x\right|$

b)

$g\left(x\right)=\frac{3}{2}\left|x\right|$

c)

$g\left(x\right)=-\frac{2}{3}\left|x\right|$

d)

$g\left(x\right)=\frac{2}{3}\left|x\right|$

36.

Choose the correct description for the transformation
$y\ =\ 3\left|x\right|$

a)

Vertical Stretch by a factor of 3

b)

Vertical Shrink by a factor of 3

c)

Vertical Compression by a factor of 1/3

d)

Vertical Compression by a factor of 1/3

37.

Does the following get wider or skinnier from the parent function y = |x|?
y = 5|x|

a)

Wider

b)

Skinnier

38.

What is the transformation for the following equation:

y = 5|x|

a)

Compression

b)

Vertical Stretch

39.

Range is:

a)

All x values, from left to right.

b)

All y values, from left to right.

c)

All y values, from bottom to top.

d)

All x values, from bottom to top.

40.

Domain is:

a)

All x values, from left to right.

b)

All y values, from bottom to top.

c)

All x values from bottom to top.

d)

All y values from left to right.

41.

How did the equation shift from the parent function? y=x+2

a)

up 2

b)

down 2

c)

steeper

d)

flipped

42.

Match the equation to its description.

a)

Right 2 and up 2

b)

Left 2 and up 2

c)

Right 2 and down 2

d)

Left 2 and down 2

43.

What is the vertex?

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

a)

(-4,3)

b)

(4,3)

c)

(-4,-3)

d)

(4,-3)

44.

Which equation would shift the quadratic function

f\left(x\right)=x^2

up 3 units and to the right 4 units.

a)

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

b)

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

c)

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

d)

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

45.

Which equation would shift the quadratic function

f\left(x\right)=x^2

3 units left and 4 units up?

a)

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

b)

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

c)

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

d)

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

46.

Describe the transformation:

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

a)

right 3, down 2

b)

up 3, left 2

c)

left 3, up 2

d)

left 3, down 2

47.

Write an equation of a quadratic that is translated down 2 units.

a)

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

b)

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

c)

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

d)

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

48.

Which quadratic would be the narrowest?

a)

$f\left(x\right)=\frac{1}{2}x^2$

b)

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

c)

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

d)

$f\left(x\right)=5x^2$

49.

What is the vertex of this equation?

y = (x + 4)² -6

Pay attention to negative signs!

a)

(4, 6)

b)

(-4, -6)

c)

(-4, 6)

d)

(4, -6)

50.

Given f(x) = (x + 6)² - 2 , how did we transform from the parent function?

a)

Horizontal shift left 6, vertical shift up 2

b)

Horizontal shift left 6, vertical shift down 2

c)

Horizontal shift right 6, vertical shift down 2

d)

Horizontal shift right 6, vertical shift up 2

51.

Given $f\left(x\right)=\frac{1}{4}x²$ how did we transform from the parent function?

a)

Vertical compression (wider)

b)

Vertical stretch (narrower)

c)

Vertical compression (wider) and reflection over x-axis

d)

Vertical stretch (narrower) and reflection over x-axis

52.

Identify the vertex and whether the graph opens up or down.

a)

(5, 2); opens up

b)

(5, 2); opens down

c)

(-5, 2); opens up

d)

(-5, 2); opens down

53.

What steps transform the graph y = x² to y = 2(x+2)² - 5?

a)

Compress by 2, shifted 2 units left and 5 down

b)

Stretch by 5, shifted 5 units left and 2 down

c)

Stretch by 2, shifted 2 units left and 5 down

d)

Compress by 5, shifted 2 units left and 2 down

54.

What steps transform the graph y = x² to y = 2(x+2)² - 5?

a)

shrink by 2, shifted 2 units left and 5 down

b)

Stretch by 5, shifted 5 units left and 2 down

c)

Stretch by 2, shifted 2 units left and 5 down

d)

shrink by 5, shifted 2 units left and 2 down

55.

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

56.

What is the domain of the graph?

a)

All real numbers

b)

No Solution

c)

y ≥ -1

or

$\left[-1,\infty\right)$

d)

x ≥ 0

or

$\left(-\infty,0\right)$

57.

What is the range of the graph?

a)

All real numbers

b)

To infinity and beyond

c)

y ≥ -1

or

$\left[-1,\infty\right)$

d)

x ≥ 0

or

$\left(-\infty,0\right]$

58.

What is the parent function for absolute values?

a)

$y=x$

b)

$y=|x|$

c)

$y=x^2$

d)

$y=2x$

59.

Describe the transformation of the equation below from the absolute value parent function.

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

a)

Left 4

b)

Right 4

c)

Up 4

d)

Down 4

60.

Describe the transformation of the equation below from the absolute value parent function.

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

a)

Left 3

b)

Right 3

c)

Up 3

d)

Down 3

61.

Describe the transformation of the equation below from the absolute value parent function.

$y=|x|+10$

a)

Shifted left 10

b)

Shifted right 10

c)

Shifted up 10

d)

Shifted down 10

62.

Describe the transformation of the equation below from the absolute value parent function.

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

a)

Left 3

b)

Right 3

c)

Up 3

d)

Down 3

63.

What is the vertex of the graph of this equation?
$y=-\left|x+6\right|$

a)

(-1, 6)

b)

(-6, 1)

c)

(-6, 0)

d)

(6, 0)

64.

Write the equation for an absolute value function that shifts down 9 from the parent function, $y=\left|x\right|$ .

a)

$y=|x|-9$

b)

$y=|x-9|$

c)

$y=-9|x|$

d)

$y=|x|+9$

65.

Write an absolute value function given the following transformations from the parent function:

Reflection across the x-axis

Vertical shift right 2 units

Horizontal shift down 7 units

a)

$y=-|x+2|-7$

b)

$y=|x-2|-7$

c)

$y=-|x-2|-7$

d)

$y=-|x-2|+7$

66.

What is the vertex of the following function? $y=2|x-3|+1$

a)

$(2,3)$

b)

$(-3,1)$

c)

$(2,-3)$

d)

$(3,1)$

67.

What is the vertex of the following function?

$y=-4|x+2|+5$

a)

$\left(2,\ 5\right)$

b)

$(-1,5)$

c)

$(-4,-2)$

d)

$(-2,5)$

68.

What is the vertex of the following equation:

$-\frac{1}{3}|x-5|+7$

a)

$\left(5,7\right)$

b)

$(-5,7)$

c)

$(7,-5)$

d)

$(7,5)$

69.

Which of the following describes the horizontal and vertical translations of the following function:

$f(x)=|x+4|-9$

a)

Left 4, up 9

b)

Left 4, down 9

c)

Right 4, up 9

d)

Right 4, down 9

70.

Describe the transformation of the equation below from the absolute value parent function.

$y=\left|x-1\right|+5$

a)

left 1, up 5

b)

left 1, down 5

c)

right 1, up 5

d)

right 1, down 5

71.

Describe the transformation of the equation below from the absolute value parent function.

$y=\left|x-2\right|+4$

a)

Left 2, up 4

b)

Right 2, up 4

c)

Left 2, down 4

d)

Right 2, down 4

72.

What is the range of the Absolute Value Parent Function?

a)

All Real Numbers

b)

(0,∞)

c)

[0,∞)

d)

(∞,0]

Transformations of Parent Functions (Abs. Value/Quadratic)

Total questions: 72

Worksheet time: 3hrs 44mins

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