Free Printable Parent Functions Part 1 Unit Review

1.

This is a _______________ function.

a)

Linear

b)

Exponential

c)

Quadratic

2.

Name the parent function.

a)

quadratic

b)

cubic

c)

square root

d)

logarithmic

3.

Name the parent function.

a)

constant

b)

quadratic

c)

linear

d)

exponential

4.

Which parent function matches the graph?

a)

y = |x|

b)

y = ∛(x)

c)

y = x²

d)

y = a⋅b^x

5.

Is the equation linear, exponential, or quadratic?

y = 2x+ 4

a)

Linear

b)

Exponential

c)

Quadratic

d)

None of the above

6.

Quadratic equations take the shape of a _______ when graphed.

a)

parabola

b)

straight line

c)

snaked line

d)

elliptical

7.

Is this a max or min?

a)

max

b)

min

c)

cannot be determined

8.

Absolute Value Function

a)

b)

9.

Square Root Function

a)

b)

c)

10.

Constant Function

a)

b)

c)

11.

Cubic Function

a)

b)

c)

12.

Reciprocal Function

a)

b)

c)

13.

Which parent function matches the graph?

a)

f(x) = x

b)

f(x)= x²

c)

f(x) = |x|

d)

f(x) = ab^x

14.

Describe the transformation that occurred

p(x) = f(x + 3)

a)

Right 3 units

b)

Vertical Stretch

c)

Up 3 units

d)

Left 3 units

15.

Describe the transformation that occurred.

h(x) = f(x) + 2

a)

up 2 units

b)

left 2 units

c)

Vertical Stretch

d)

right 2 units

16.

Describe the transformation that occurred.

w(x) = f(x - 7)

a)

Down 7

b)

up 7

c)

right 7

d)

vertical compression

17.

Describe the transformation that occurred

k(x) = f(x) - 9

a)

vertical compression

b)

down 9

c)

left 9

d)

right 9

18.

Given f(x) = (x-3)² + 5. What transformations took place from the original function f(x)?

a)

Left 3 up 5

b)

Right 3 down 5

c)

Left 3 down 5

d)

Right 3 up 5

19.

Describe the transformations of f(x) when compared to the parent function. f(x)=(x+7)²

a)

horizontal shift left 7 units

b)

horizontal shift right 7 units

c)

vertical shift up 7 units

d)

vertical shift down 7 units

20.

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

21.

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)

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

22.

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

23.

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

24.

Choose the equation that best matches the graphed function.

a)

$f(x)=|x-4|+3$

b)

$f(x)=|x-3|+4$

c)

$f(x)=|x-4|-3$

d)

$f(x)=|x+4|+3$

25.

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)

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

26.

Describe the transformation that occurred

g(x) =2f(x)

a)

Up 2 units

b)

vertical compression

c)

vertical stretch

d)

Right 2 Units

27.

Describe the transformation that occurred

h(x) = 1/5f(x)

a)

Up 5 Units

b)

vertical compression

c)

vertical stretch

d)

Down 5 Units

28.

Which equation describes the transformation of shifting f(x)=x³ seven units up?

a)

x³+7

b)

x³-7

c)

(x-7)³

d)

(x+7)³

29.

If the blue graph is
f(x) = x²
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

30.

Identify the critical points of the following function:
g(x)=2x³-3x²

a)

x=-1,1

b)

x=0,0

c)

x=0,-1

d)

x=0,1

31.

What is the relative maximum value?

a)

y = 4

b)

y = 2

c)

y = 1

d)

y = -1

32.

Find the *critical numbers of

f(x) = x² + 2x + 1

*Coordinate of x

a)

x = -1

b)

x = 2

c)

x = -1, 0

d)

x = 0

33.

Find all the critical numbers of

f(x) = 2x³ – 6x² + 12

Select ALL that apply.

a)

x= 4

b)

x= 0

c)

x= -2

d)

x= 2

34.

What are the local maxima of this graph?

a)

local maximum at (2.2, 3.9)

b)

local maximum at (-8, 5)

c)

local maximum at (5, -8)⋃(3.9, 2.2)

d)

local maximum at (-8, 5)⋃(2.2, 3.9)

35.

List the types of intervals that the graph demonstrates in order.

a)

decreasing, constant, increasing, constant

b)

increasing, decreasing, constant

c)

increasing, constant, increasing, constant

d)

increasing, constant, decreasing, constant

36.

Where is the function increasing?

a)

(4, ∞)

b)

(−4, ∞)

c)

(6, ∞)

d)

4 < x < 6

37.

Where is the decreasing?

a)

( −∞, −2.55) U (0, 2.55)

b)

(∞, −6.25) U (36, −6.25)

c)

(−∞, ∞)

d)

(−∞, 0)

38.

What is the absolute max?

a)

(0, 36)

b)

(−2.55, −6.55), (2.55, −6.55)

c)

(−∞, ∞)

d)

None

39.

Over what interval is this function constant?

a)

(-5, ∞)

b)

(-3, 4)

c)

(4, ∞)

d)

-5

40.

When is this function increasing in interval notation?

a)

(-3, 3)

b)

(0, 5)

c)

(0, 55)

d)

(-5, 0)

41.

the point (-1, 0) is an ...

a)

Absolute Maximum

b)

Absolute Minimum

c)

Local Maximum

d)

Local Minimum

42.

What are the local minimum of this graph?

a)

local minimum at (-2.5, -3.3)

b)

local minimum at (-2.5,-3.3)U(5, -2.5)

c)

local minimum at (5, -2.5)

d)

local minimum at (-3.3, -2.5)⋃(-2.5, 5)

43.

What is the inverse of the given coordinates: (1, 2) (3, 8) (-3, 6)

a)

(1, 2) (3, 8) (-3, 6)

b)

(1, 2) (8, 3) (-3, 6)

c)

(-1, -2) (-3, -8) (3, -6)

d)

(2, 1) (8, 3) (6, -3)

44.

Are these the graphs of two inverse functions?

a)

Yes

b)

No

c)

No way to tell

45.

Suppose you are given a table of values. When creating a table for the inverse graph you must...?

a)

Switch the x and y

b)

Solve for x

c)

Plot the coordinates

d)

Potato

46.

What's the name of the inverse of g(x)?

a)

f(x)

b)

f^-1(x)

c)

y

d)

g^-1(x)

47.

Find the inverse of f(x) = -4x - 12

a)

f^-1(x) = 4x - 3

b)

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

c)

f^-1(x) = 1/4x + 3

d)

f^-1(x) = -4x - 3

48.

Match the following functions to their inverses

a)

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

1.

$f^{-1}\left(x\right)=\frac{x+7}{2}$

b)

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

2.

$f^{-1}\left(x\right)=\frac{x-2}{7}$

c)

$f\left(x\right)=\sqrt[]{x-7}+2$

3.

$f^{-1}\left(x\right)=\left(x-2\right)^2+7$

d)

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

4.

$f^{-1}\left(x\right)=\sqrt[]{x+7}-2$

49.

If a function contains the points

(-6,3) (-4,5) (1, -3) (5,-4)

Graph the inverse function's points

50.

Find the inverse of

f(x)=(x+12)²

a)

f^-1(x)= $\sqrt[]{x}-12$

b)

f^-1(x)= $\sqrt[]{x-12}$

c)

f^-1(x)=whTA

d)

f^-1(x)=X-12

51.

Find the inverse of

f(x)= $\sqrt[]{x-3}$

a)

f^-1(x)=x²+3

b)

f^-1(x)=x²-3

c)

f^-1(x)=x²

d)

too hard

52.

Find the inverse of

f(x)= $\sqrt[]{x}-3$

a)

f(x)=x+3

b)

f^-1(x)= $\left(x+3\right)^2$

c)

f^-1(x)=x+x

d)

f^-1(x)=x+5

53.

Are these functions inverses of each other?

a)

Yes

b)

No

54.

a)

A.

b)

B.

c)

C.

d)

D.

55.

Find the inverse of $f\left(x\right)=-\frac{3}{4}x+5$

a)

$f^{-1}\left(x\right)=5\left(x-\frac{4}{3}\right)$

b)

$f^{-1}\left(x\right)=-\frac{3}{4}\left(x-5\right)$

c)

$f^{-1}\left(x\right)=-\frac{4}{3}\left(x-5\right)$

d)

$f^{-1}\left(x\right)=-5\left(x-\frac{3}{4}\right)$

56.

a)

Inverse Functions

b)

Not Inverse Functions

57.

a)

Inverse Functions

b)

Not Inverse Functions

58.

To prove two functions are inverses of each other, both f(g(x)) and g(f(x)) should equal...

a)

1

b)

x

c)

0

d)

y

59.

$f\left(x\right)\ =\ 5x\ -\ 5$ $g\left(x\right)\ =\ \frac{1}{5}x\ +\ 1$

Use composition of functions to determine if f(x) and g(x) are inverse functions.

a)

yes

b)

no

60.

in what value of x does the following function is discontinuous?

a)

3

b)

-3

c)

6

d)

-6

61.

The function f(x) = x²-2x+1, continuous to the interval [-7,7]

a)

TRUE

b)

FALSE

62.

Which of the following best describes the continuity at x = -4?

a)

Continuous

b)

Removable Point Discontinuity

c)

Infinite Discontinuity

d)

Jump Discontinuity

63.

Which of the following best describes the continuity at x = 5?

a)

Continuous

b)

Removable Point Discontinuity

c)

Infinite Discontinuity

d)

Jump Discontinuity

64.

Which of the following best describes the continuity at x = 5?

a)

Continuous

b)

Removable Point Discontinuity

c)

Infinite Discontinuity

d)

Jump Discontinuity

65.

What is the End behavior on the left side

a)

x →-∞, y→∞

b)

x →∞, y→-∞

c)

x →-∞, y→-∞

d)

x →∞, y→∞

66.

What is the End behavior on the right side

a)

x →-∞, y→∞

b)

x →-∞, y→-∞

c)

x →∞, y→∞

d)

x →∞, y→-∞

67.

What is the end behavior of the function

a)

as x →⁻∞,y→⁻∞, as x →∞, y→⁻∞

b)

as x→⁻∞, y→∞, as x →∞, y→∞

c)

as x→⁻∞, y→0, as x →∞, y→∞

d)

as x→⁻∞, y→⁻∞, as x →∞,y→∞

68.

y = -x²

a)

down and down

b)

down and up

c)

up and down

d)

up and up

69.

y = x²

a)

down and down

b)

down and up

c)

up and down

d)

up and up

70.

Which function has this end behavior?

a)

-x²-3x+1

b)

-x³+2x²+3

c)

x⁴+3x³-4x+1

d)

x⁵-4x⁴+2x²-1

71.

Determine the end behavior of the graph.
There are arrows.

a)

As x→ -∞, y→ +∞
As x→ +∞, y→ +∞

b)

As x→ -∞, y→ -∞
As x→ +∞, y→ -∞

c)

As x→ -∞, y→ -∞
As x→ +∞, y→ +∞

d)

As x→ -∞, y→ +∞
As x→ +∞, y→ -∞

72.

what the leading coefficient

a)

Postive

b)

Negative

c)

Even

d)

Odd

73.

what the is the degree of the polynomial

a)

Postive

b)

Negative

c)

Even

d)

Odd

74.

Match the following End Behavior to their Graphs

a)

1.

Degree is Odd, Leading Coefficient is Negative

b)

2.

Degree is Odd, Leading Coefficient is Positive

c)

3.

Degree is Even, Leading Coefficient is Negative

d)

4.

Degree is Even, Leading Coefficient is Positive

75.

What is the degree of the polynomial?

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

a)

4

b)

3

c)

2

d)

1

76.

Check all the even degree polynomials:

a)

b)

c)

d)

e)

77.

What is the degree?

a)

Positive

b)

Negative

c)

Odd

d)

Even

78.

What is the leading coefficient?

a)

Positive

b)

Negative

c)

Odd

d)

Even

79.

Which one means up

a)

$f\left(x\right)\rightarrow-\infty$

b)

$f\left(x\right)\rightarrow\infty$

80.

Which one means left

a)

$x\rightarrow-\infty$

b)

$x\rightarrow\infty$

81.

What is the end behavior of

$g\left(x\right)=-2x^6+2x^5-12x-6$

a)

up/down

b)

down/up

c)

down/down

d)

up/up

82.

What is the end behavior of

$h(x)=-8x^5+22x^4-4x^3+11x-9$

a)

up/down

b)

down/up

c)

up/up

d)

down/down

83.

Which of the following intervals is the function positive?

a)

$x<-3$

b)

$x>-3$

c)

$x<1$

d)

$x>1$

84.

Which of the following intervals is the function negative?

a)

$x<-3$

b)

$x>-3$

c)

$x<1$

d)

$x>1$

85.

Identify where the function is negative.

a)

$x\ >-3$

b)

All Real Numbers

c)

$-3<x<3$

d)

$x<-3,\ x>3$

86.

Identify where the function is positive.

a)

$-3<x<3$

b)

All Real Numbers

c)

$x<-3,\ \ x>3$

87.

Identify where the function is negative.

a)

$-5<x<0,\ x\ >6$

b)

$x<-5,\ x\ >6$

c)

$-5<x<6$

d)

$x<-5,\ 0<x<6$

Parent Functions Part 1 Unit Review

Total questions: 87

Worksheet time: 6hrs 44mins

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