Free Printable PC U3 L1-L8 Parent Functions and Transformations

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 quadratic function:

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

a)

Shift up 2 units

b)

Shift down 2 units

c)

Shift right 2 units

d)

Shift left 2 units

3.

Describe the transformation from the parent square root function:

$y=\sqrt[]{x+4}$

a)

Shift up 4 units

b)

Shift down 4 units

c)

Shift right 4 units

d)

Shift left 4 units

4.

Describe the transformation from the parent cubic function:

$y=-x^3+3$

* Select TWO answers *

a)

Shift up 3 units

b)

Shift down 3 units

c)

Reflection over the y-axis

d)

Reflection over the x-axis

5.

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

6.

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

7.

Describe the transformation from the parent square root function:

$y=2\ \sqrt[]{x-5}$

* Select TWO answers *

a)

Vertical stretch

b)

Vertical shrink

c)

Translation 5 units right

d)

Translation 5 units left

8.

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

9.

Describe the transformation from the parent cubic function:

$y=\left(x+6\right)^3-4$

* Select TWO answers *

a)

Translation 6 units right

b)

Translation 6 units left

c)

Translation 4 units up

d)

Translation 4 units down

10.

Describe the transformation

a)

left 2 up 5

b)

right 2 up 5

c)

left 2 down 5

d)

right 2 down 5

11.

Write the equation to match the graph. The parent function is y=|x|

a)

y = Ix + 2I - 1

b)

y = -Ix + 2I - 1

c)

y = -Ix - 2I - 1

d)

y = -Ix + 1I - 2

12.

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

13.

What is the equation of the PARENT function?

a)

f(x) = 2^x

b)

f(x) = x³

c)

f(x) = |x|

d)

f(x) = x

14.

What type of function is shown?

a)

cube root

b)

square root

c)

logarithm

d)

exponential

15.

Which parent function matches the graph?

a)

y = |x|

b)

y = ∛(x)

c)

y = x²

d)

y = a⋅b^x

16.

What type of function is shown?

a)

absolute value

b)

quadratic

c)

linear

d)

exponential

17.

What type of function is shown?

a)

linear

b)

quadratic

c)

square root

d)

absolute value

18.

Which parent function matches the graph?

a)

f(x) = x

b)

f(x)= x²

c)

f(x) = |x|

d)

f(x) = ab^x

19.

What type of function is shown?

a)

Exponential

b)

square root

c)

quadratic

d)

cube root

20.

Which parent function matches the graph?

a)

f(x) = √(x)

b)

f(x) = ∛(x)

c)

f(x) = |x|

d)

f(x) = a⋅b^x

21.

Name the parent function.

a)

constant

b)

quadratic

c)

linear

d)

exponential

22.

Name the parent function.

a)

constant

b)

square root

c)

linear

d)

absolute value

23.

Name the parent function.

a)

linear

b)

exponential

c)

logarithmic

d)

cubic

24.

Name the parent function.

a)

constant

b)

linear

c)

quadratic

d)

cube root

25.

Name the parent function.

a)

cubic

b)

cube root

c)

exponential

d)

quadratic

26.

Name the parent function.

a)

cube root

b)

square root

c)

quadratic

d)

linear

27.

Name the parent function.

a)

cubic

b)

square root

c)

rational

d)

cube root

28.

Name the parent function.

a)

quadratic

b)

cubic

c)

square root

d)

logarithmic

29.

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.

30.

Range 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.

31.

If the blue function is f(x)=x², then the red function must be

a)

g(x)=x²-5

b)

g(x)=x²+5

c)

g(x)=(x-5)²

d)

g(x)=(x+5)²

32.

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

33.

Which graph shows this transformation?

a)

b)

c)

d)

34.

Describe the transformation from the parent cubic function:

$y=-x^3+3$

* Select ALL correct answers *

a)

Shift up 3 units

b)

Shift down 3 units

c)

Reflection over the y-axis

d)

Reflection over the x-axis

35.

Describe the transformation from the parent absolute value function:

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

* Select ALL correct 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

36.

What colored graph is the parent function?

a)

Red

b)

Blue

c)

Black

d)

Purple

37.

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

38.

Describe the parent graph transformation

a)

stretch by 1/2, left 1, down 3

b)

stretch by 1/2, right 1, down 3

c)

compression by 1/2, left 1, down 3

d)

compression by 1/2, right 1, down 3

39.

What is the range of the graph?

a)

1 ≤ x ≤ 5

b)

1 < x < 5

c)

1 ≤ y ≤ 5

d)

1 < y < 5

40.

What is the range of the graph?

a)

1 ≤ x ≤ 5

b)

1 < x < 5

c)

1 ≤ y ≤ 5

d)

1 < y < 5

41.

On what interval is the graph decreasing?

a)

(∞, 3)

b)

(3, -∞)

c)

(3, ∞)

d)

(-∞, 3)

42.

On which interval is the graph increasing?

a)

(-5,-3)

b)

(-3,-1)

c)

(1,4)

d)

(5,∞)

43.

On which interval is the graph decreasing?

a)

(-5,-3)

b)

(-3,-1)

c)

(1,4)

d)

(5,∞)

44.

On which interval is the graph constant?

a)

(-5,-3)

b)

(-3,-1)

c)

(1,4)

d)

(-∞,-5)

45.

What is the minimum?

a)

None

b)

(0,4)

c)

(3,1)

d)

y = -1

46.

Where is the function increasing?

a)

(-∞,5)

b)

(-∞,0)

c)

(-∞,2)

d)

(0,2

47.

What is the range of the function?

a)

(-∞,5]

b)

(-∞,5)

c)

(-∞,2]

d)

(-∞,2)

48.

Describe the function's end behavior.

a)

$As\ x\rightarrow-\infty,\ y\rightarrow-\infty$
$As\ x\rightarrow\infty,\ y\rightarrow-\infty$

b)

$As\ x\rightarrow-\infty,\ y\rightarrow-\infty$
$As\ x\rightarrow\infty,\ y\rightarrow\infty$

c)

$As\ x\rightarrow-\infty,\ y\rightarrow\infty$
$As\ x\rightarrow\infty,\ y\rightarrow-\infty$

d)

$As\ x\rightarrow-\infty,\ y\rightarrow\infty$
$As\ x\rightarrow\infty,\ y\rightarrow\infty$

49.

Identify the intervals where the function is positive and where it is negative.

a)

positive (-1, ∞) and negative (-∞, -1)

b)

positive nowhere and negative (-1, -4)

c)

positive (-∞,-3) and (1,∞) and negative (-3,1)

d)

positive (-∞,∞) and negative (-4,∞)

50.

Identify the function's domain and range.

a)

domain (-∞,∞) and range (-∞,∞)

b)

domain (-∞, ∞) and range (-4,∞)

c)

domain (-∞,∞) and range [-4,∞)

d)

domain [-3, 1] and range [-4,∞)

51.

What is the x-intercept of the exponential function?

a)

(0,1)

b)

(0,0)

c)

There is not one

52.

Given y=3^xdetermine the y-intercept

a)

(0,1)

b)

(0,3)

53.

What is the increasing interval for the function below?

a)

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

b)

$\left(-\infty,2\right)$

c)

$\left(-\infty,6\right)$

d)

$\left(-6,6\right)$

54.

What is/are the decreasing interval(s) for the function shown?

a)

$\left(2,\ 4\right)\ and\ \left(8,\ \infty\right)$

b)

$\left(-\infty,\ 1\right)\ and\ \left(8,\ \infty\right)$

c)

$\left(-\infty,1\right),\ \left(-3,\ 1\right)\ and\ \left(8,\ \infty\right)$

d)

$\left(-\infty,\ 1\right),\ \left(2,\ 4\right)\ and\ \left(8,\ \infty\right)$

55.

What is the increasing interval on the function shown?

a)

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

b)

$\left(-\infty,\ 2\right)$

c)

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

d)

$\left(1,\ \infty\right)$

56.

What is the increasing interval on the function shown?

a)

$\left(-\infty,\ -3\right)$

b)

$\left(-\infty,\ -4\right)$

c)

$\left(-4,\ \infty\right)$

d)

$\left(-3,\ \infty\right)$

57.

Describe the end behavior of the graph.

a)

x →∞, y→∞ and x→∞, y→⁻∞

b)

x →∞, y→∞ and x→⁻∞, y→∞

c)

x →∞, y→∞ and x→⁻∞, y→0

d)

x →∞,y→0 and x→∞, y→⁻∞

58.

Describe the end behavior of the graph.

a)

x → ∞, y→ ∞ and x→∞, y→⁻∞

b)

x → ∞, y→ ∞ and x→⁻∞, y→∞

c)

x → ∞, y→ ∞ and x→⁻∞, y→ 0

d)

x → ∞,y→ ∞and x→ ⁻∞, y→ ⁻∞

59.

What is the range of the following graph?

a)

-5, -1, 0 , 1, 5

b)

-4, -2, 0, 3, 6

c)

(-4, 1) ( 6, 0)

d)

(6, 0)

60.

What is the range of the following graph?

a)

all real numbers

b)

all integers

c)

any real number greater than zero

d)

it can not be determined

61.

What is the domain?

a)

x = 2

b)

−∞ < x < ∞

c)

y = 2

d)

none of these

62.

What is the interval of increase of this function?

a)

(1, +∞)

b)

None

c)

(2, +∞)

d)

(-∞, +∞)

63.

What is the interval of decrease for this function?
There are no arrows.

a)

(-5, 3)

b)

(-∞,+∞)

c)

[-2, 6]

d)

(-2, 6)

64.

Identify where the function is increasing and where it is decreasing.

a)

increasing (-1, ∞) and decreasing (-∞,-1)

b)

increasing (-∞, -1) and decreasing (-1, ∞)

c)

increasing (-∞,∞) and decreasing nowhere

d)

increasing (-1, -4) and decreasing (-3, 1)

65.

Is this graph a function or not a function?

a)

Function

b)

Not a Function

66.

How would you describe the behavior of this function on the domain interval $-1\le x\le1$ ?

a)

increasing

b)

decreasing

c)

constant

67.

Find the function's x- and y-intercepts.

a)

x-int (0,-3) and (0,1)

y-int (-4,0)

b)

x-int (-3,0) and (1,0)

y-int (0,-4)

c)

x-int (-4, 1)

y-int (-4, ∞)

d)

x-int (-3,0) and (1,0)

y-int (0,-3)

68.

Find the function's maximum and minimum points

a)

no maximum

minimum (-4,-1)

b)

no minimum

maximum (-3, 1)

c)

no maximum

minimum (-1,-4)

d)

maximum (-3,1)

minimum (0,-3)

69.

Identify where the function is increasing and where it is decreasing.

a)

increasing x > -1 and decreasing x<-1

b)

increasing x < -1 and decreasing x > -1

c)

increasing ꓣ and decreasing nowhere

d)

increasing -1 < x < 4 and decreasing -3 < x < 1

70.

Identify the intervals where the function is positive and where it is negative.

a)

positive x > -1 and negative x < -1

b)

positive nowhere and negative -4 < x < -1

c)

positive x < -3 and x > 1 and negative -3 < x < 1

d)

positive R and negative x < -4

71.

What was the initial height of the projectile?

a)

50

b)

0

c)

200

d)

6.75

72.

What is the maximum height?

a)

200

b)

50

c)

3

d)

0

73.

Which coordinate is a relative maximum for the graph?

a)

None

b)

(0,4)

c)

(3,1)

d)

(1, -1)

74.

Which coordinate is a relative minimum of the graph?

a)

None

b)

(0,4)

c)

(3,1)

d)

(1, -1)

75.

What is the domain of the function?

a)

$x≤5$

b)

$x<5$

c)

$x≤2$

d)

$x<2$

76.

What is the range of the function?

a)

$y≤5$

b)

$y\ <\ 5$

c)

$y≤2$

d)

$y\ <\ 2$

77.

Which ordered pair could represent a
y-intercept on a graph?

a)

(6, 0)

b)

(0, 4)

c)

(-1, 3)

d)

(2, 0)

78.

a)

Function

b)

Not a Function

79.

a)

Function

b)

Not a Function

80.

On what interval is the graph decreasing?

a)

$y>3$

b)

$y<3$

c)

$y\ge3$

d)

$y\le3$

81.

On which interval is the graph increasing?

a)

$-5\le x\le-3$

b)

$-3\le x\le-1$

c)

$1\le x\le4$

d)

$x\ge5$

82.

What is the RANGE?

a)

$-3<y\le3$

b)

All Real Numbers

c)

$-4\le y\le5$

d)

$y\le-4$

83.

What is the DOMAIN?

a)

$x\ge0$

b)

$x<0$

c)

All Real Numbers

d)

{0, 1, 2, 3, 4,...}

84.

Describe the function between $x=-2$ and $x=2$ .

a)

Increasing

b)

Decreasing

c)

Constant

85.

Identify the domain of the function.

a)

$-4≤x≤4$

b)

$R$

c)

$x≥4$

d)

$x≤4$

86.

Identify the range of the function.

a)

$-4.5≤y≤2$

b)

$R$

c)

$y≥-4.5$

d)

$y≤2$

87.

Describe the transformation that occurred.

g(x) = f(x - 7)

a)

Down 7

b)

up 7

c)

right 7

d)

vertical compression

88.

Describe the transformation of the equation below from the absolute value parent function. SELECT ALL THAT APPLY $g\left(x\right)=\frac{1}{2}f\left(x+3\right)-2$

a)

right 3

b)

left 3

c)

Down 2

d)

Shrink by 1/2

e)

stretch by 2

89.

Describe the transformations that maps f(x) to g(x) = - f(x + 6) - 10

a)

Reflect over y-axis
Shifted down 10 units
Shifted left 6 units

b)

Reflect over x-axis
Shifted up 10 units
Shifted left 6 units

c)

Reflect over y-axis
Shifted up 10 units
Shifted right 6 units

d)

Reflect over x-axis
Shifted down 10 units
Shifted left 6 units

90.

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

a)

g(x)=f(x)-5

b)

g(x)=f(x)+5

c)

g(x)=f(x-5)

d)

g(x)=f(x+5)

91.

Describe the transformation from dotted to solid.

a)

g(x) = f(x + 4)

b)

g(x) = f(x - 4)

c)

g(x) = f(x) + 4

d)

g(x) = f(x) - 4

92.

Match the following

a)

f(x+6)

1.

The line shifted 6 units to the left.

b)

f(x-6)

2.

The line shifted 6 units to the right.

c)

f(x)-6

3.

The line shifted 6 units down.

d)

f(x+3)

4.

The line shifted 3 units to the left.

e)

f(x)+3

5.

The line shifted 3 units up.

93.

What is the effect on the graph of the linear parent function, f(x) = x, when f(x) is replaced by f(x- 7)?

Complete the sentence by selecting the correct answers from the drop-down menus.

The graph of the line (a) (b) 7 units.

Choose from the below words

shifts horizontally

up

down

left

right

shifts vertically

94.

Create a function given the following transformations for $f\left(x\right)=2^x$ :

Shift left 1

Shift down 2

Reflect over the x-axis

Vertical stretch by 3

$g\left(x\right)=$ ____

Don't include g(x) in answer

95.

The parent function of a square root is represent by $f\left(x\right)=\sqrt[]{x}$

For each function, determine how the parent function was transformed.

$f\left(x\right)=-\sqrt[]{x-2}$ (a)

$f\left(x\right)=\sqrt[]{x}+1$ (b)

$f\left(x\right)=\sqrt[]{x+3}-7$ (c)

$f\left(x\right)=-\sqrt[]{x}$ (d)

Choose from the below words

Vertical Reflection Only

Horizontal Translation Only

Vertical Translation Only

Vertical Reflection and Vertical Translation

Vertical Refl., Horizontal & Vertical Trans

Vertical Reflection & Horizontal Translation

Vertical Translation & Horizontal Translation

96.

The function $f\left(x\right)=x^3$ was (a) by a factor of 1/3, shifted (b) 2 units, and shifted (c) 4 units to create the function $g\left(x\right)\ =\ \frac{1}{3}f\left(x-2\right)+4$ .

Choose from the below words

vertically compressed

right

up

vertically stretched

left

down

97.

Match the following

a)

x³ + 2

1.

Vertical translation 2 up

b)

(x-2)³

2.

Horizontal translation 2 right

c)

2x³

3.

Vertical stretch

d)

(x+2)³

4.

Horizontal translation 2 left

e)

0.2x³

5.

Vertical compress

98.

Write the equation for a cubic function that has been vertically compressed by a factor of 3, vertically shifted 5 units down, and horizontally shifted 7 units left.

99.

Describe the transformations of the cubic parent function, $f\left(x\right)=x^3$ , that will result in the graph of the function $f\left(x\right)=-1.5\left(3x-5\right)^3+2$

Choose one of each.

Vertical Stretch or compress: (a)

Horizontal stretch or compress: (b)

Reflection over x-axis or y-axis: (c)

Translation left or right: (d)

Translation up or down: (e)

Choose from the below words

Stretch

Compress

x-axis

y-axis

Right

Left

Up

Down

PC U3 L1-L8 Parent Functions and Transformations

Total questions: 99

Worksheet time: 8hrs 49mins

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