Free Printable Characteristics of Functions

1.

What is the domain of the graph?

a)

y≥1

b)

x ≥ 1

c)

All real numbers

d)

none of these

2.

What is the range of the graph?

a)

y≥1

b)

x≥1

c)

All real numbers

d)

none of these

3.

What is the domain of the graph?

a)

-7 ≤ x < 5

b)

-3 ≤ x < 1

c)

-3 ≤ y < 1

d)

-7 ≤ y < 5

4.

What is the range of the graph?

a)

-7 ≤ x < 5

b)

-3 ≤ x < 1

c)

-3 ≤ y < 1

d)

-7 ≤ y < 5

5.

What is the domain?

a)

-3 < y ≤ 3

b)

-4 ≤ y ≤ 5

c)

-4 ≤ x ≤ 5

d)

-3 < x ≤ 3

6.

What is the range?

a)

-3 < y ≤ 3

b)

-4 ≤ y < 5

c)

-4 ≤ y ≤ 5

d)

-3 < y ≤ 3

7.

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)

8.

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,∞)

9.

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 all real numbers and decreasing nowhere

d)

increasing x < -3 or x > 1 and decreasing -3 < x < 1

10.

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

a)

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

b)

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

c)

x-int (1,∞) and y-int (-∞,-1)

d)

x-int none and y-int (-1,1)

11.

Where is the function positive and where is it negative?

a)

positive x > 1 and negative x < 1

b)

positive x > 0 and negative x < 0

c)

positive all real numbers and negative nowhere

d)

positive x < 1 and negative x > 1

12.

Where is the function increasing and decreasing?

a)

increasing all real numbers and decreasing nowhere

b)

increasing nowhere and decreasing all real numbers

c)

increasing x > 1 and decreasing x < 1

d)

increasing x < 1 and decreasing x > 1

13.

Where is the function positive and where is it negative?

a)

positive -2<x<1 and x > 3

negative x < -2 and 1<x<3

b)

positive x < -1 and x > 2

negative -1 < x < 2

c)

positive -1 < x < 4

negative 2 < x < -2

d)

positive x < 3 and 1<x<-2

negative 3<x<1 and x>-2

14.

What is the domain of the absolute value function?

a)

(4, 0)

b)

(0, 4)

c)

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

d)

$\left[4,\infty\right)$

15.

What is the range of the absolute value function?

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

a)

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

b)

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

c)

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

d)

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

16.

Identify the x-intercept of the graph.

a)

(-4, 0)

b)

(0, -2)

c)

(0, -4)

d)

(-2, 0

17.

Identify the x-intercept(s)

a)

(-1, 0)

b)

(5, 0)

c)

(5, 0) & (-1, 0)

d)

(-1, 0) & (0, 1)

18.

What is/are the x-intercept(s) of the absolute value function?

a)

(0, 4)

b)

none

c)

(4, 0)

d)

[4, infinity)

19.

What are the x- intercepts?

a)

x= 0 and x= -4

b)

x= 0 and x= 4

c)

y= 0

d)

x= 2

20.

Where is the function positive?

a)

$0<x<4$

b)

$at\ the\ vertex\ \left(2,4\right)$

c)

$y\le4$

d)

$-\infty<x<\infty$

21.

Is the graph increasing or decreasing?

a)

Increasing

b)

Decreasing

c)

Both; increasing if x < 3, and decreasing is x > 3

d)

Both; decreasing if x < 3, and increasing is x > 3

22.

Is the function increasing or decreasing?

a)

increasing

b)

decreasing

c)

increasing if x > 0 and and decreasing if x < 0

d)

neither

23.

What are the domain and the range of the function?

a)

domain (-∞,∞) and range (-∞,∞)

b)

domain (∞,-∞) and range (∞,-∞)

c)

domain (-∞, 3] and range [3,∞)

d)

domain (-∞,1] and range [1,∞)

24.

Is the function increasing or decreasing?

a)

increasing

b)

decreasing

c)

both

d)

neither

25.

On what interval is the graph decreasing?

a)

$y>3$

b)

$y<3$

c)

$y>1.5$

d)

$y<4.5$

26.

What is the DOMAIN?

a)

$x\ge0$

b)

$x<0$

c)

All Real Numbers

d)

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

27.

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

28.

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

29.

Identify the function's domain and range.

a)

domain -∞ to ∞ and range -∞ to ∞

b)

domain -∞ to ∞ and range 4 to ∞

c)

domain -∞ to ∞ and range -4 to ∞

d)

domain -3 to 1 and range -4 to ∞

30.

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

a)

25

b)

30

c)

35

d)

40

31.

What is the interval of increase?

a)

All Real Numbers

b)

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

c)

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

d)

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

32.

What is the interval of increase?

a)

All Real Numbers

b)

$\left(0,\ 2\right)$

c)

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

d)

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

33.

Identify the range of the function.

a)

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

b)

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

c)

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

d)

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

34.

For the pictured function, at which interval is it decreasing?

a)

(-∞, 2)

b)

(-2, 0)

c)

(0, ∞)

d)

(-3, 1)

35.

Which ordered pair could represent a y-intercept?

a)

(-1, 0)

b)

(2, 4)

c)

(0,4)

d)

(-2, 4)

36.

What is the y-intercept of the graph?

a)

(-2,5)

b)

(1,0)

c)

(0,1)

d)

(-3.104, 0)

37.

When is the function decreasing?

a)

(30, 55)

b)

(40, 60)

c)

(15, 40)

d)

(60, -40)

38.

What is f(0)?

a)

$-1$

b)

$2$

c)

$4$

d)

$-5$

39.

Find the x values in which f(x) > 0 [Find where it is positive.]

a)

(-1, 1)

b)

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

c)

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

d)

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

40.

Identify the decreasing interval:

a)

(0, 4)

b)

(1, 0) U (1, 4)

c)

(-1, 1)

d)

(-∞, -1) U (1, ∞)

41.

Determine the interval in which this function is DECREASING.

a)

(-3, ∞)

b)

(-3, ∞)

c)

(-∞, -4)

d)

(-∞, -3)

42.

Determine the interval in which this function is INCREASING.

a)

(-4, ∞)

b)

(-3, ∞)

c)

(∞, -3)

d)

(-∞, -4)

43.

What are the x-intercepts?

a)

(0, 0) and (2, 0)

b)

(-4, 0) and (0, 0)

c)

(2, 0) and (3, 0)

d)

(0, 0) and (4, 0)

44.

Which is true?

a)

f(0) = 2

b)

f(-2) = 6

c)

f(3) = 0

d)

f(-3) = 1

45.

What is the end behavior of the function?

a)

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

b)

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

c)

$x\rightarrow-\infty,\ y\rightarrow3$

d)

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

46.

Which one(s) describe the end behavior of the graph. Choose all that apply.

a)

$x\rightarrow\infty,\ y\rightarrow\infty$

b)

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

c)

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

d)

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

47.

What is the y-intercept of the function?

a)

2

b)

3

c)

1

d)

-2

48.

Is the relation a function? Why.

a)

Yes, because the x-value 11 has two y-values pair with it.

b)

Yes, because each x-value has only one y-value paired with it.

c)

No, because the x-value 11 has two y-values pair with it.

d)

No, because each x-value has only one y-value paired with it.

49.

Which set of values is a function?

a)

(9,5) (10,5) (9,-5) (10,-5)

b)

(3,4) (4,-3) (7,4) (3, 8)

c)

(6,-5) (7, -3) (8, -1) (9, 1)

d)

(2, -2) (5, 9) (5, -7) (1, 4)

50.

All of the x values or inputs are called what?

a)

Domain

b)

Range

c)

Relation

d)

Function

51.

All of the y values or outputs are called what?

a)

Domain

b)

Range

c)

Relation

d)

Function

52.

What is the definition of a function?

a)

Has inputs and outputs

b)

Every input has only ONE output

c)

Inputs have different outputs every time

d)

x-values and y-values

53.

Is it a function?

a)

It IS a function.

b)

It IS NOT a function

54.

What is the y-intercept?

a)

(0,7)

b)

(0, 0)

c)

(0,1)

d)

(0, 2)

55.

What are all the x-intercepts?

a)

(-2.55, 0), (2.55, 0)

b)

(-3,0), (-2,0), (2,0), (3,0)

c)

(0, 36)

d)

(-∞,∞)

56.

Translate the function notation into a coordinate point.

$f\left(-1\right)=5$

a)

$\left(-1,5\right)$

b)

$\left(1,5\right)$

c)

$\left(5,1\right)$

d)

$\left(5,-1\right)$

57.

Translate the coordinate pair into function notation.

\left(0,8\right)

a)

$f\left(0\right)=8$

b)

$f\left(0\right)=-8$

c)

$f\left(8\right)=0$

d)

$f\left(-8\right)=0$

58.

Given the function
$f\left(x\right)=x+3$

Evaluate:

f\left(-2\right)

a)

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

b)

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

c)

$f\left(-2\right)=5$

d)

$f\left(-2\right)=-5$

59.

Given
$g\left(x\right)=4x-2$

Evaluate:

g\left(-7\right)

a)

$g\left(-7\right)=-30$

b)

$g\left(-7\right)=-26$

c)

$g\left(-7\right)=-36$

d)

$g\left(-7\right)=26$

60.

Given:
$w\left(x\right)=-10x-5$

Evaluate:
$w\left(1\right)$

a)

$w\left(1\right)=-15$

b)

$w\left(1\right)=-5$

c)

$w\left(1\right)=5$

d)

$w\left(1\right)=15$

61.

Given:
$f\left(x\right)=6x$

Find x when

f\left(x\right)=-24

a)

$x=-4$

b)

$x=4$

c)

$x=-144$

d)

$x=-6$

62.

Given:
$g\left(x\right)=3x-5$

Find x when $g\left(x\right)=4$

a)

$x=3$

b)

$x=-3$

c)

$x=7$

d)

$x=-3$

63.

Given:
$h\left(x\right)=14-8x$

Find x when

h\left(x\right)=-2

a)

$x=2$

b)

$x=-2$

c)

$x=30$

d)

$x=-30$

64.

Given the graph,

find:

f\left(2\right)

a)

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

b)

$f\left(2\right)=4$

c)

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

d)

$f\left(2\right)=0$

65.

Given the graph,

find:

f\left(4\right)

a)

$f\left(4\right)=3$

b)

$f\left(4\right)=1$

c)

$f\left(4\right)=2$

d)

$f\left(4\right)=0$

66.

Given the graph,

find:

f\left(6\right)

a)

$f\left(6\right)=3$

b)

$f\left(6\right)=1$

c)

$f\left(6\right)=2$

d)

$f\left(6\right)=0$

67.

Given the graph,

find:

f\left(7\right)

a)

$f\left(7\right)=3$

b)

$f\left(7\right)=1$

c)

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

d)

$f\left(7\right)=0$

68.

Given the graph,

find:

f\left(0\right)

a)

$f\left(0\right)=7$

b)

$f\left(0\right)=1$

c)

$f\left(0\right)=2$

d)

$f\left(0\right)=0$

69.

Given the graph,

find the value of x when:

f\left(x\right)=0

a)

$x=1$

b)

$x=0$

c)

$x=7$

d)

$x=2$

70.

Given the graph,

find the value of x when:

f\left(x\right)=5

a)

$x=5$

b)

$x=0$

c)

$x=3$

d)

$x=2$

71.

Given the graph,

find the value of x when

f\left(x\right)=5

a)

$x=7$

b)

$x=6$

c)

$x=5$

d)

$x=3$

72.

Given the graph,

find the value of x when

f\left(x\right)=2

a)

$x=7$

b)

$x=1$

c)

$x=5$

d)

$x=4$

73.

Is this graph a function or not a function?

a)

Function

b)

Not a Function

74.

Select ALL of the functions.

a)

{ (a,z) , (b,z) , (c,z) }

b)

c)

d)

75.

Select ALL of the functions.

a)

{ (a,z) , (b,z) , (c,z) }

b)

c)

d)

76.

Evaluate the function for f(9) if $\ f\left(x\right)=\frac{3}{5}x+8$ .

a)

$\frac{67}{5}$

b)

$-\frac{13}{5}$

c)

$-\frac{67}{5}$

d)

$\frac{13}{5}$

77.

Is the following graph a function? Explain.

a)

Yes, because no x-value repeats.

b)

Yes, because they are individual dots.

c)

No, because the x repeats.

d)

No, because it is not a line.

78.

Is this graph a function or not a function?

a)

Function

b)

Not a Function

79.

Is this a function?

a)

Function

b)

Not a Function

80.

Is this mapping a function or not a function?

a)

Function

b)

Not a Function

Characteristics of Functions

Total questions: 80

Worksheet time: 26mins

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