Free Printable Functions & Properties REVIEW

1.

Over what interval is this function constant?

a)

-5 < x < ∞

b)

-3 < x < 4

c)

4 < x < ∞

d)

-5

2.

When is the velocity decreasing?

a)

0 < t < 60

b)

40 < t < 60

c)

15 < t < 40

d)

-40 < t < 0

3.

When is this function increasing?

a)

-2.5 < x < 2.5

b)

0 < x < 5

c)

0 < x < 55

d)

-5 < x < 0

4.

How long did it take Sam to get to school?

a)

5 minutes

b)

20 minutes

c)

1.25 km

d)

1.25 minutes

5.

How long did Sam sit on the bench and wait for the bus?

a)

5 min

b)

10 min

c)

15 min

d)

20 min

6.

Over which interval of time is this person returning home?

a)

8:00 < x < 9:00

b)

9:00 < x < 9:30

c)

9:30 < x < 11:00

d)

12:00 < x < 13:00

7.

Which statement is true about this graph?

a)

This function is always constant

b)

This function is always increasing

c)

This function is never increasing

d)

This function is both increasing and decreasing

8.

At what time did this Kayak trip begin?

a)

15:00

b)

12:00

c)

0 km

d)

11:00

9.

Which statement is true about this function?

a)

The function is never constant

b)

The function is always increasing

c)

The function is never decreasing

d)

The function increases on the interval 11:00 < x < 15:00

10.

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)

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

11.

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

a)

$\left(-3,\ 1\right)$

b)

$\left(4,\ 8\right)$

c)

$\left(-\infty,1\right)\ \cup\ \left(-3,\ 1\right)$

12.

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

a)

$\left(4,\ 8\right)$

b)

$\left(-3,\ 1\right)$

c)

$\left(-\infty,1\right)\ \ \cup\ \left(-3,\ 1\right)$

d)

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

13.

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

a)

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

b)

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

c)

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

d)

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

14.

What is the decreasing interval(s) on the function shown?

a)

$\left(-7,\ -6\right)\ \cup\ \left(-2,\ 4\right)$

b)

$\left(-7,\ 0\right)\ \ \cup\ \left(-2,\ 4\right)$

c)

$\left(-7,\ -6\right)\ \ \cup\ \left(-2,\ 0\right)$

d)

$\left(-7,\ 0\right)\ \cup\left(4,\ 5\right)$

15.

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)

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

16.

What is the decreasing interval on the function shown?

a)

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

b)

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

c)

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

d)

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

17.

What is the decreasing interval on the function shown?

a)

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

b)

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

c)

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

d)

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

18.

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)

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

19.

What is the increasing interval(s) on the function shown?

a)

$\left(-\infty,\ -15\right)\cup\left(9,\ -15\right)$

b)

$\left(-2,\ 9\right)\ \cup\ \left(2,\ \infty\right)$

c)

$\left(-\infty,\ -2\right)\cup\ \left(0,\ 2\right)$

d)

$\left(-2,\ 0\right)\cup\ \left(2,\ \infty\right)$

20.

What is the decreasing interval(s) on the function shown?

a)

$\left(-\infty,\ -15\right)\ \cup\ \left(9,\ -15\right)$

b)

$\left(-2,\ 9\right)\ \ \cup\left(2,\ \infty\right)$

c)

$\left(-\infty,\ -2\right)\cup\left(0,\ 2\right)$

d)

$\left(-2,\ 0\right)\cup\ \left(2,\ \infty\right)$

21.

A roller coaster park is open from May to October each year. The graph shows the number of park visitors each day over the course of its season.

Describe what Segment 1 means in the context of this situation?

a)

The attendance during the first weeks of May was constant (the same number of people visited each day).

b)

The attendance increased very quickly over this period of time.

c)

The attendance decreases over this period of time.

d)

The attendance increases slowly and comes to a peak at the end of this period of time.

22.

A roller coaster park is open from May to October each year. The graph shows the number of park visitors each day over the course of its season.

Describe what Segment 2 shows in this context.

a)

The attendance during the first weeks of May was constant (the same number of people visited each day).

b)

The attendance increased very quickly over this period of time.

c)

The attendance decreases over this period of time.

d)

The attendance increases slowly and comes to a peak at the end of this period of time.

23.

A roller coaster park is open from May to October each year. The graph shows the number of park visitors each day over the course of its season.

What happens during segment 3?

a)

The attendance during the first weeks of May was constant (the same number of people visited each day).

b)

The attendance increased very quickly over this period of time.

c)

The attendance decreases over this period of time.

d)

The attendance increases slowly and comes to a peak at the end of this period of time.

24.

A roller coaster park is open from May to October each year. The graph shows the number of park visitors each day over the course of its season.

What happens during segments 4 and 5?

a)

The attendance during the first weeks of May was constant (the same number of people visited each day).

b)

The attendance increased very quickly over this period of time.

c)

The attendance decreases over this period of time.

d)

The attendance increases slowly and comes to a peak at the end of this period of time.

25.

Oliver is hiking a trail that takes him straight up a mountain. He starts his hike at 8 am at the base of the mountain. The distance, d, in miles, that Oliver is from the base of the mountain t hours after starting his hike is shown in the graph.

Between what times is the slope of the graph positive?

a)

The slope of the graph is positive between x = 0 and x = 3 and also between x = 5 and x = 7

b)

The slope is positive between x = 3 and x = 5

26.

Oliver is hiking a trail that takes him straight up a mountain. He starts his hike at 8 am at the base of the mountain. The distance, d, in miles, that Oliver is from the base of the mountain t hours after starting his hike is shown in the graph.

What does it mean to have a positive slope in this context?

a)

Oliver is hiking up the mountain

b)

Oliver is hiking down the mountain

c)

Oliver is taking a break from hiking

27.

Oliver is hiking a trail that takes him straight up a mountain. He starts his hike at 8 am at the base of the mountain. The distance, d, in miles, that Oliver is from the base of the mountain t hours after starting his hike is shown in the graph.

What does it mean to have a 0 slope in this context? (between x = 3 and x = 5 the slope is 0)

a)

Oliver is hiking up the mountain

b)

Oliver is hiking down the mountain

c)

Oliver is taking a break from hiking

28.

Antonio and Juan are in a 4-mile bike race. The graph shows the distance of each racer, in miles, as a function of time, in minutes.

Who wins the race? How do you know?

a)

Juan because he gets to 4 miles first (x = 13)

b)

Antonio because he gets to 4 miles first (x = 15)

c)

they tie because they both get to 4 miles at the same time

29.

The figure below gives the depth of the water at Montauk Point, New York, for a day in November.

How many high tides took place on this day?

a)

1

b)

2

c)

3

d)

0

30.

The figure below gives the depth of the water at Montauk Point, New York, for a day in November.

How many LOW tides took place on this day?

a)

1

b)

2

c)

3

d)

0

31.

Find the local maximum and minimum

a)

Local max at x = -3

Local min at x = -3

b)

Local max at x = 1

Local min at x = -3

c)

Local max at x = -3

Local min at x = 1

d)

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

32.

Identify the local minimum

a)

x = 8

b)

x = 4

c)

$\infty$

d)

x = 2

33.

Identify the global (or absolute) maximum.

a)

-2

b)

1

c)

$\infty$

d)

$-\infty$

34.

What is the location of the absolute maximum for the graphed function?

a)

x = 1

b)

x = 3

c)

x = 4

d)

x = 5

e)

Does Not Exist

35.

What is the value of the absolute minimum for the following function?

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

a)

x = -4

b)

x = 0

c)

x = 2

d)

x = 4

e)

Does Not Exist

36.

What is the location of the relative maximum within the given interval of the graphed function?

-5\le x\le0

a)

x = -4

b)

x = -2

c)

x = 0

d)

x = 3

e)

Does Not Exist

37.

What are the extrema of the graph?

a)

Max = (2, -3), (1, 2)

Min = (-3, -1), (-1, 4)

b)

Max = (-3, -1), (-1, 4)

Min = (2, -3), (1, 2)

c)

Max = (-1, -3), (4, -1)

Min = (-3, 2), (2, 1)

d)

Max = (-3, 2), (2, 1)

Min = (-1, -3), (4, -1)

38.

How many extrema are there in this graph?

a)

2 max, 2 min

b)

3 max, 2 min

c)

2 man, 3 min

d)

3 increasing intervals, 2 decreasing intervals

e)

2 increasing intervals, 3 decreasing intervals

39.

How many extrema (max and mins) are in the picture?

a)

2

b)

3

c)

4

d)

5

40.

What is the relative max?

a)

x = 0

b)

x = -2.55

c)

(-∞, ∞)

d)

None

41.

Write the inequality in interval notation.

a)

[-4, -1)

b)

(-4, -1)

c)

(-4, -1]

d)

[-4, -1]

42.

Write the following in interval notation

-7 ≤ x < 8

a)

(-7, 8)

b)

[-7, 8)

c)

[-7, 8]

d)

(-7, 8]

43.

Write the following in interval notation

x < 8

a)

[8, ∞)

b)

(8, -∞)

c)

(-∞, 8]

d)

(-∞, 8)

44.

Look at the graph. Write the interval notation for the graph.

a)

(-2,5)

b)

(-∞,-2)⋃(5,∞)

c)

[-2,5]

d)

(-∞,-2]∪[5,∞)

45.

Can you use the symbols [ or ]
with infinity?

a)

Yes

b)

No

46.

What interval notation does the number line graph represent?

a)

[∞, -5)

b)

(∞, -5)

c)

[-5, ∞)

d)

(-5, ∞)

47.

When you graph an inequality, you use a closed dot when you use which symbols?

a)

≤, ≥

b)

<, >

c)

≤, <

d)

≥, >

48.

Would you use a closed or open circle to graph x < 3?

a)

Closed

b)

Open

49.

What inequality is graphed?

a)

2 < x < 4

b)

2 ≤ x ≤ 4

c)

x > 2 or x < 4

d)

x ≥ 2 or x ≤ 4

50.

Write the interval notation for the graph?

a)

[-3, 2)

b)

-3<x<2

c)

(-∞, -3] U (2, ∞)

d)

x > 2 or x < -3

51.

Express the following in Interval Notation
-8 ≤ x < 8

a)

[-8, 8]

b)

[-8,8)

c)

(-8, 8]

d)

(-8, 8)

52.

Express the following in Interval Notation
-9 < x ≤ -4

a)

[-9, -4]

b)

(-9,-4]

c)

[-9, -4]

d)

(-9,-4)

53.

What is the domain of the function?

a)

(3, ∞)

b)

[-3, ∞)

c)

(-∞, 4]

d)

(-∞, 4)

54.

What is the domain?

a)

(-3 , 3)

b)

[-4, 5]

c)

(-4, 5)

d)

(-3, 3]

55.

What is the range?

a)

(-3, 3)

b)

[-4, 5)

c)

[-4 , 5]

d)

(-3 , 3]

56.

What is the domain of the graph?

a)

[1,∞)

b)

(-∞,1]

c)

(-∞,∞)

d)

[-∞,∞]

57.

What is the range of the graph?

a)

[1, ∞)

b)

(1, ∞)

c)

(-∞, ∞)

d)

none of these

58.

What is the domain of the graph?

a)

[ -∞, ∞]

b)

(-∞,∞)

c)

[-3 , 3]

d)

[-15, 9]

59.

What is the range of the graph?

a)

[-15, 9]

b)

(-∞, ∞)

c)

(-15, ∞)

d)

[-15, ∞)

60.

Write the following in interval notation
x < 8

a)

(8, ∞)

b)

(8, -∞)

c)

(-∞, 8)

d)

[-∞, 8]

61.

Write the interval notation as an inequality. (-∞, 5]

a)

x > 5

b)

x ≥ 5

c)

x < 5

d)

x ≤ 5

62.

The set of all y-values used to graph a function are called the ____.

a)

Domain

b)

Range

c)

Relation

d)

Function

63.

What is the range of the graph?

a)

(-∞,∞)

b)

[0,∞)

c)

(0,5)

d)

[-1,∞)

64.

In interval notation, positive and negative ∞ are always closed in by ______.

a)

( ) Parentheses

b)

[ ] Square Brackets

c)

{ } Curly Brackets

65.

In set notation, the infinity symbols are not used. Instead "_____" is used to represent a graph that uses all real numbers.

a)

R

b)

Z

c)

I

d)

A

66.

DOMAIN is found by reading the ends of a graph from ___ to ___.

a)

Right to left

b)

Left to right

c)

Bottom to top

d)

Top to bottom

67.

RANGE is found by reading the ends of a graph from ___ to ___.

a)

Right to left

b)

Left to right

c)

Bottom to top

d)

Top to bottom

68.

The set of all x-values used to graph a function are called the ____.

a)

Domain

b)

Range

c)

Relation

d)

Function

69.

Write the following range in set builder notation:

(4, ∞).

a)

{y | y > 4}

b)

{y | y > 4}

c)

{x | x < 4}

d)

{x | x > 4}

70.

Given {x| x ≥ 6}, the domain of a function in set builder notation, which of the following rewrites it in interval notation?

a)

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

b)

$\left[6,\infty\right)$

c)

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

d)

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

71.

What are the Vertical Asymptotes of...

a)

x = 0, -5

b)

x=0, 5

c)

x = 2, -7

d)

x = -2, 7

72.

What is the hole?

a)

x= 4

b)

x= -4

c)

x= 5

d)

x= -5

73.

What is the Vertical Asymptotes?

a)

x= -5

b)

x= 5

c)

x= 6

d)

x= -6

74.

Which asymptote(s) are determined by looking at the denominator?

a)

vertical

b)

horizontal

c)

slant

d)

none

75.

Find the vertical asymptotes and holes of the function.

a)

Holes: None;

VA: x = 1, -3

b)

Holes: x = -3;

VA: x = 1

c)

Holes: x = -3, 1

VA: None

d)

Holes: x = 1

VA: x = -3

76.

Find the hole of the function.
x²- 9x+20
___________
4x² - 12x- 40

a)

x =5

b)

x=0

c)

x=4

d)

x=-2

77.

Where is there a hole on the graph of the function?

a)

x = 2

b)

x = -2

c)

There are no holes.

d)

x = 5

78.

How many vertical asymptotes does the function have?

a)

None

b)

1

c)

2

d)

3

79.

Find the vertical asymptotes and holes of the function.

a)

Holes: None;

VA: x = 1, -3

b)

Holes: x = -3;

VA: x = 1

c)

Holes: x = -3, 1

VA: None

d)

Holes: x = 1

VA: x = -3

80.

State the vertical asymptote.

a)

x = -2/5

b)

x = -5/2

c)

x = -5

d)

x = 2

81.

Find the coordinates of the hole.

a)

(-3, -3)

b)

(-3, 3)

c)

(3, -3)

d)

(3, 3)

82.

A hole occurs when....

a)

You wear pants that are too tight.

b)

A factor from the numerator cancels with a factor in the denominator.

c)

The degree of the numerator is one more than the degree of the denominator.

d)

The denominator cannot be factored.

83.

Where is the hole?

a)

x= 4

b)

x= -4

c)

x= 5

d)

x= -5

84.

What is the Vertical Asymptotes?

a)

x= -5

b)

x= 5

c)

x= 2

d)

x= -2

85.

Name any holes of the function.

a)

x=0

b)

none

c)

x=1

86.

What is the domain of this graph?

a)

$x\ge0$ ( $\left[0,\ \infty\right)$ )

b)

$x<0$

c)

All real numbers ( $\left(-\infty,\ \infty\right)$ )

d)

None of the above

87.

What is the range of this parent graph? Choose the best answer.

a)

All nonnegative numbers $y\ge0\ \left(\left[0,\ \infty\right)\right)$

b)

All real numbers ( $\left(-\infty,\ \infty\right)$ )

c)

All negative numbers $y<0\ \left(\left(-\infty,\ 0\right)\right)$

d)

All of the above

88.

What is the range of this graph?

a)

$y\ge0$ ( $\left[0,\ \infty\right)$ ) (nonnegative numbers)

b)

All real numbers $\left(-\infty,\ \infty\right)$

c)

All negative numbers ( $y<0$ ) ( $\left(-\infty,\ 0\right)$

d)

None of the above

89.

What is the range of the function?

a)

All negative numbers and/or 0 ( $y\le0$ ) $\left(-\infty,\ 0\right]$

b)

Nonnegative numbers $y\ge0$ $\left[0,\ \infty\right)$

c)

All real numbers $\left(-\infty,\ \infty\right)$

d)

All numbers $x\ne0$

90.

What is the end behavior as $x\rightarrow-\infty$ ?

a)

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

b)

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

c)

$f\left(x\right)\rightarrow0$

d)

None of the above

91.

What is the end behavior as $x\rightarrow-\infty$ ?

a)

$f\left(x\right)\rightarrow0$

b)

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

c)

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

d)

$f\left(x\right)\rightarrow9$

92.

What is the end behavior as $x\rightarrow-\infty$ ?

a)

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

b)

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

c)

$f\left(x\right)\rightarrow0$

d)

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

93.

What is the domain of this graph?

a)

$x\ge0$ ( $\left[0,\ \infty\right)$ )

b)

All $x>0$

c)

All real numbers ( $\left(-\infty,\ \infty\right)$ )

d)

None of the above

94.

Determine the boundedness of the function graphed.

a)

Bounded Above

b)

Bounded Below

c)

Bounded

d)

Unbounded

95.

Determine the boundedness of the function graphed.

a)

Bounded Above

b)

Bounded Below

c)

Bounded

d)

Unbounded

96.

Determine the boundedness of the function graphed.

a)

Bounded Above

b)

Bounded Below

c)

Bounded

d)

Unbounded

97.

Determine the boundedness of the function graphed.

a)

Bounded Above

b)

Bounded Below

c)

Bounded

d)

Unbounded

98.

Determine the boundedness of the function graphed.

a)

Bounded Above

b)

Bounded Below

c)

Bounded

d)

Unbounded

99.

Determine the boundedness of the function graphed.

a)

Bounded Above

b)

Bounded Below

c)

Bounded

d)

Unbounded

100.

Determine the boundedness of the function graphed.

a)

Bounded Above

b)

Bounded Below

c)

Bounded

d)

Unbounded

101.

Determine the boundedness of the function graphed.

a)

Bounded Above

b)

Bounded Below

c)

Bounded

d)

Unbounded

102.

Determine the boundedness of the function graphed.

a)

Bounded Above

b)

Bounded Below

c)

Bounded

d)

Unbounded

103.

Determine the boundedness of the function graphed.

a)

Bounded Above

b)

Bounded Below

c)

Bounded

d)

Unbounded

104.

The function shown in the graph is:

a)

even

b)

odd

c)

neither even nor odd

d)

both even and odd

105.

The function in the graph is:

a)

even

b)

odd

c)

neither even nor odd

d)

both even and odd

106.

The function shown in the graph is:

a)

even

b)

odd

c)

neither odd nor even

d)

both odd and even

107.

Is the graph an even, odd, or neither function?

a)

Even

b)

Odd

c)

Neither

108.

Determine algebraically: Is the function even, odd, or neither?

f(x) = 4x³

a)

Even

b)

Odd

c)

Neither

109.

Determine algebraically: Is the function even, odd, or neither?

f(x) = x² + 2

a)

Even

b)

Odd

c)

Neither

110.

Determine algebraically: Is this an even, odd, or neither function?

f(x) = x⁴ + x²

a)

Even

b)

Odd

c)

Neither

111.

Is the table even, odd or neither?

a)

Even

b)

Odd

c)

Neither

112.

Is the table even, odd or neither?

a)

Even

b)

Odd

c)

Neither

113.

Which table is odd?

a)

b)

c)

d)

114.

What is the domain?

a)

(-∞, +∞)

b)

(-4, +∞)

c)

[-1.5, 1.5]

d)

(-∞, -4]

115.

What is the domain of the function?

a)

(3, ∞)

b)

[-3, ∞)

c)

(-∞, 4]

d)

(-∞, 4)

116.

What is the range?

a)

[-7,6]

b)

(-7,6)

c)

(-8, 2)

d)

[-8,2]

117.

Which graphs have a range of (-∞, 3]

a)

I and II

b)

I and III

c)

II and III

d)

I , II and III

118.

What is the domain?

a)

(-3 , 3)

b)

[-4, 5]

c)

(-4, 5)

d)

(-3, 3]

119.

Given the function f(x) = x²+2x+10, find f(3).

a)

3

b)

20

c)

22

d)

25

120.

Determine algebraically if each of the following functions is even, odd, or neither. f(x) = x⁵-5x³+1

a)

even

b)

odd

c)

neither

121.

Determine algebraically if each of the following functions is even, odd, or neither. f(x) = 2x⁴+x²-6

a)

even

b)

odd

c)

neither

122.

What is the DOMAIN?

a)

(-∞, +∞)

b)

(-∞, 1)

c)

(-∞, 1]

d)

(-∞, 0) U (0, +∞)

123.

Is this mapping a function or not a function?

a)

Function

b)

Not a Function

124.

Is this graph a function or not a function?

a)

Function

b)

Not a Function

125.

Is this table a function or not a function?

a)

Function

b)

Not a Function

Functions & Properties REVIEW

Total questions: 125

Worksheet time: 4hrs 1mins

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