Free Printable Unit 5 Review - Lessons 1 through 4

1.

Does the graph have a maximum or minimum?

a)

max

b)

min

c)

neither

d)

both

2.

Find the x-intercept(s) of the graph shown.

(Pick all answers that apply)

a)

(-3.3, 0)

b)

(5.6, 0)

c)

(-5, 0)

d)

(0, 4)

3.

Find the y-intercept(s) of the graph shown.

a)

(-3.3, 0)

b)

(5.6, 0)

c)

(-5, 0)

d)

(0, 4)

4.

Find the interval(s) of increase of the graph shown.

a)

(-6, -4)

b)

(-4, -2)

c)

(-2, 2)

d)

(2, 5)

e)

(5, 6)

5.

Find the interval(s) of decrease of the graph shown.

(There is more than one answer)

a)

(-6, -4)

b)

(-4, -2)

c)

(-2, 2)

d)

(2, 5)

e)

(5, 6)

6.

Find the interval(s) where the graph remains constant.

a)

(-6, -4)

b)

(-4, -2)

c)

(-2, 2)

d)

(2, 5)

e)

(5, 6)

7.

What are the zeros?

a)

0 and 2

b)

-4 and 0

c)

2 and 3

d)

0 and 4

8.

What is the minimum of this graph?

a)

(-2,6)

b)

(-0.5,-3.5)

c)

(-1,-3)

d)

(3,0)

9.

How many roots does the function have?

a)

None

b)

1

c)

2

d)

3

10.

Where is the function increasing?

a)

(-∞,5]

b)

(-∞,0]

c)

(-∞,2]

d)

[0,2]

11.

Which function has a maximum at (2, 0)?

a)

b)

c)

d)

12.

What is the interval of increase?

a)

From 0 to 3

b)

From 3 to 7

c)

From 25 to 40

d)

From 50 to 25

13.

What is the interval of decrease?

a)

From 0 to 3

b)

From 3 to 7

c)

From 25 to 40

d)

From 50 to 25

14.

Let's call the graph f(x). Find f(5) = ___

a)

25

b)

30

c)

35

d)

40

15.

Look at the function that is graphed, what are the maximum and minimum values of this function?

a)

maximum 15, minimum -5

b)

maximum 25, minimum -15

c)

maximum 25, minimum -10

d)

maximum 30, minimum -10

16.

What are the roots of the function?

a)

3

b)

-6

c)

-1 and 3

d)

-6, -1, and -3

17.

Identify the relative maximum:

a)

(0, 3)

b)

(4, 1)

c)

(3, 0)

d)

(1, 4)

18.

What is the domain of the function?

a)

95 to 116 degrees

b)

0 to 24

c)

0 to 120

d)

0 to 24 hours

19.

What is the range of the function?

a)

95 to 116 degrees

b)

0 to 24

c)

0 to 120 degrees

d)

0 to 24 hours

20.

What is the absolute maximum?

a)

116 degrees

b)

120 degrees

c)

24 hrs

d)

0 hrs

21.

What does the absolute maximum mean?

a)

it's the highest point on the graph

b)

it's the highest temperature for the day

c)

it's the biggest number for the day

22.

What is the y-intercept?

a)

100

b)

0

c)

115

d)

110

23.

In how many intervals is this graph decreasing?

a)

2

b)

3

c)

4

d)

5

24.

Where could we say this graph is increasing?

a)

It is increasing from -3 to 0

b)

It is increasing from 0 to 2

c)

It is increasing from 2 to 4

d)

It is increasing from 4 to infinity

e)

It is increasing at the point (0, 3)

25.

What is the constant interval for this function?

a)

(0, 5)

b)

(8, 3)

c)

[0, 8]

d)

(3, 8)

26.

Determine the range of the graph.

a)

(1, +∞)

b)

[1, +∞)

c)

(2, +∞)

d)

[2, +∞)

27.

Determine the end behavior of the graph.

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→ -∞

28.

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→ -∞

29.

a)

The end behavior of the graph is x →∞, y→∞ and x→∞, y→⁻∞

b)

The end behavior of the graph is x →∞, y→∞ and x→⁻∞, y→∞

c)

The end behavior of the graph is x →∞, y→∞ and x→⁻∞, y→∞

d)

The end behavior of the graph is The end behavior of the graph is x →∞,y→⁻∞ and x→∞, y→⁻∞

30.

In the above graph complete the following end behavior:
As x --> -∞, f(x) --> ____
As x --> +∞, f(x) --> ____

a)

-∞
-∞

b)

+∞
-∞

c)

-∞
+∞

d)

+∞
+∞

31.

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

a)

Left 3 and up 5

b)

Right 3 and down 5

c)

Left 3 and down 5

d)

Right 3 and up 5

32.

If the blue graph is f(x) (the original function) and the red graph is the transformation, what is the equation of the red graph?

a)

-f(x)

b)

f(-x)

c)

f^-1(x)

d)

f(2x)

33.

Identify the transformations.

a)

horizontal shift to the left 2 and vertical stretch by a factor of 3

b)

horizontal shift to the right 2 and vertical stretch by a factor of 3

c)

horizontal shift to the right 2 and vertical shrink by a factor of 3

d)

horizontal shift to the left 2 and vertical shrink by a factor of 3

34.

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

35.

g(x)=-f(x)
Describe the transformation to f(x) that results in g(x).

a)

f(x) has been reflected over the x-axis.

b)

f(x) has been reflected over the y-axis.

36.

Which transformation maps the graph of
f(x) = x² to the graph of g(x) = (x + 4)²?

a)

a translation shifting f(x) 4 units up

b)

a translation shifting f(x) 4 units down

c)

a translation shifting f(x) 4 units to the left

d)

a translation shifting f(x) 4 units to the right

37.

A student graphed f(x) = x and g(x) = f(x) - 12. Which statement is true?

a)

The graph of f is shifted 12 units to the right to create the graph of g.

b)

The graph of f is shifted 12 units down to create the graph of g.

c)

The graph of f is shifted 12 units up to create the graph of g.

d)

The graph of f is shifted 12 units to the left to create the graph of g.

38.

How did we transform from f(x) =x²tog(x) = -3x²

a)

reflection in x-axis and vertical shift down

b)

reflection x-axis and vertical stretch

c)

horizontal stretch

d)

reflection x-axis and vertical compression

39.

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

40.

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|

41.

Describe the transformation

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

a)

3 Units Up

b)

3 Units Down

c)

3 Units Left

d)

3 Units Right

42.

Describe the transformation

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

a)

2 Units Up

b)

2 Units Down

c)

2 Units Left

d)

2 Units Right

43.

Describe the transformation

$f\left(x+5\right)$

a)

5 Units Up

b)

5 Units Down

c)

5 Units Left

d)

5 Units Right

44.

Describe the transformation

$f\left(x\right)-6$

a)

6 Units Up

b)

6 Units Down

c)

6 Units Left

d)

6 Units Right

45.

Describe the transformation

$f\left(x\right)-6$

a)

6 Units Up

b)

6 Units Down

c)

6 Units Left

d)

6 Units Right

46.

Describe the transformations

$g\left(x+4\right)-6$

a)

4 Units Left

6 Units Up

b)

4 Units Left

6 Units Down

c)

4 Units Right

6 Units Up

d)

4 Units Right

6 Units Down

47.

Describe the transformations

$-g\left(x\right)+2$

a)

Reflected across the x-axis

2 Units Up

b)

Reflected across the x-axis

2 Units Down

c)

Reflected across the y-axis

2 Units Up

d)

Reflected across the y-axis

2 Units Down

48.

Describe the transformation

$3h\left(x\right)$

a)

Vertically Stretched by a factor of 3

b)

Vertically Compressed by a factor of 3

c)

Horizontally Stretched by a factor of 3

d)

Horizontally Stretched by a factor of 3

49.

Describe the transformation

$h\left(\frac{1}{3}x\right)$

a)

Vertically Stretched by a factor of $\frac{1}{3}$

b)

Vertically Compressed by a factor of $\frac{1}{3}$

c)

Horizontally Stretched by a factor of $\frac{1}{3}$

d)

Horizontally Stretched by a factor of $\frac{1}{3}$

50.

Describe the transformations

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

a)

Reflected across the x-axis

4 Units Left

b)

Reflected across the x-axis

4 Units Down

c)

Reflected across the y-axis

4 Units Left

d)

Reflected across the y-axis

4 Units Down

51.

Describe the transformations that maps
y = g(x) to y = - g(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

52.

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

a)

Left 3 and up 5

b)

Right 3 and down 5

c)

Left 3 and down 5

d)

Right 3 and up 5

53.

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

a)

Translated left 2 units

b)

Reflected over x-axis

c)

Vertical Stretch by a factor of 2 and reflected over x-axis

d)

Vertical Shrink by a Factor of 2 and reflected over the x-axis

54.

Describe the parent graph transformation

a)

Vertical stretch by 1/2, left 1, down 3

b)

Vertical stretch by 1/2, right 1, down 3

c)

Vertical Shrink by 1/2, left 1, down 3

d)

Vertical Shrink by 1/2, right 1, down 3

55.

a)

y = √(x + 2) + 3

b)

y = √(x − 2) + 3

c)

y = √(x − 3) + 2

d)

y = √(x + 3) + 2

56.

Which is an equation that shifts the graph of the function above to the left 5 units?

a)

b)

c)

d)

57.

Describe the transformation.

a)

Left 1unit, Reflect over x-axis, up 2 units

b)

Left 1unit, Reflect over y-axis, down 2 units

c)

Right 1 unit, Reflect over x-axis, up 2 units

d)

Right 1unit, Reflect over y-axis, up 2 units

58.

If f(x) = 3x-1 and g(x) = x²+2,

what is (f ° g)(x) ?

a)

3x² +5

b)

x² +1

c)

3x² +1

d)

3x² +6

59.

If f(x) = 5x and g(x) = 2x-1,

what is the composition f(g(x)) ?

a)

10x-1

b)

10x-5

c)

5x²-1

d)

5x²-5

60.

If f(x) = x-1 and g(x) = 2x,

what is and g(f(x)) ?

a)

2x²-1

b)

2x-1

c)

2x-2

d)

x-2

61.

f(x) = 3x + 10
g(x) = x - 2
Find f(g(5))

a)

19

b)

23

c)

-10

d)

None of these.

62.

Find g(- 2).

a)

12

b)

-2

c)

-24

d)

18

63.

p(x) = 3x + 4
q(x) = 2x²
Find p(q(x))

a)

10x²

b)

18x² + 4

c)

6x² + 4

64.

Evaluate f(x)=-2x+13 for f(10)

a)

-7

b)

1

c)

-8

d)

7

65.

Given
f(x)= 2x² + 5x - 17, find f(-1).

a)

f(-1) = -20

b)

f(-1) = -24

66.

For f(x) = 2x²-1, what is and (f ° f)(-2) ?

a)

7

b)

97

c)

13

d)

6

67.

g(x)=3x+4
h(x)=3x-1
Find (g∘h)(x)

a)

-9x+11

b)

4x²+4x

c)

9x+1

d)

9x+11

68.

f(x) = 3x + 10
g(x) = x - 2
Find f(g(5))

a)

19

b)

23

c)

-10

d)

None of these.

69.

g(a) = 4a + 1

h(a) = -3a + 2

Find g(h(1))

a)

3

b)

-3

c)

21

d)

-21

70.

g(x)=3x+4
h(x)=3x-1
Find g(h(x))

a)

-9x+11

b)

4x²+4x

c)

9x+1

d)

9x+11

71.

a)

-1

b)

1

c)

-1/3

d)

-5/3

72.

a)

9 - √17

b)

4

c)

2

d)

√8

73.

a)

b)

c)

d)

74.

a)

b)

c)

d)

75.

a)

9 - √17

b)

4

c)

2

d)

√8

76.

If $f\left(x\right)=2x$ and $g\left(x\right)=2x^2-1$ find $f\left(g\left(x\right)\right)$

a)

$4x^2-1$

b)

$4x^2-2$

c)

$8x^2-1$

d)

$16x^2-1$

77.

If $f\left(x\right)=2x$ and $g\left(x\right)=2x^2-1$ find $f\left(g\left(3\right)\right)$

a)

34

b)

71

c)

35

d)

142

78.

If $f\left(x\right)=x^2-1$ and $g\left(x\right)=4x-3,$ find $\left[f\circ g\right]\left(3\right).$

a)

$43$

b)

$91$

c)

$80$

d)

$26$

79.

If $f\left(x\right)=x^2-1$ and $g\left(x\right)=4x-3,$ find $g\left(1\right).$

a)

$-4$

b)

$1$

c)

$-9$

d)

$4$

80.

If $f\left(x\right)=x^2-1$ and $g\left(x\right)=4x-3,$ find $f\left(2\right).$

a)

$\frac{2}{3}$

b)

$-5$

c)

$6$

d)

$3$

Unit 5 Review - Lessons 1 through 4

Total questions: 80

Worksheet time: 4hrs 0mins

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