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Characteristics of Linear and Nonlinear Functions

Total questions: 110

Worksheet time: 58mins

Name
Class
Date
1.

Identify the Domain or Range 1. ( f(x) = x + 5 ) What is the domain?

a)

A. All real numbers

b)

B. x ≥ 0

c)

C. x ≤ 5

d)

D. x ≠ 5

2.

Identify the Domain or Range 2. ( f(x) = x + 5 ) Range?

a)

A. All real numbers

b)

B. y ≥ 0

c)

C. y ≤ 5

d)

D. y ≠ 5

3.

Identify the Domain or Range 3. ( f(x)=x2f(x) = x^2 ) Domain?

a)

A. All real numbers

b)

B. x ≥ 0

c)

C. x ≤ 0

d)

D. x ≠ 0

4.

Identify the Domain or Range 4. ( f(x) = x2x^2 ) Range?

a)

A. y ≥ 0

b)

B. y ≤ 0

c)

C. all real numbers

d)

D. y = 0

5.

Identify the Domain or Range 5. ( f(x) = sqrt{x} ) Domain?

a)

A. x ≥ 0

b)

B. x ≤ 0

c)

C. all real numbers

d)

D. x ≠ 0

6.

( f(x) = sqrt(x) ) Range?

a)

y ≥ 0

b)

y ≤ 0

c)

y ≠ 0

d)

all real numbers

7.

( f(x) = |x| ) Domain?

a)

A. All real numbers

b)

B. x > 0 only

c)

C. x < 0 only

d)

D. x = 0 only

8.

( f(x) = |x| ) Range?

a)

y ≥ 0

b)

all real numbers

c)

y ≤ 0

d)

y = 0 only

9.

( f(x) = x - 3 ) Domain?

a)

A. all real numbers

b)

B. x ≥ 3

c)

C. x ≤ 3

d)

D. x ≠ 3

10.

( f(x) = x - 3 ) Range?

a)

A. all real numbers

b)

B. y ≥ 3

c)

C. y ≤ 3

d)

D. y ≠ 3

11.

Given the table: x: 1 2 3 4 f(x): 5 6 7 8 Domain?

a)

A. {1,2,3,4}

b)

B. {5,6,7,8}

c)

C. all real numbers

d)

D. {6,7}

12.

Using the same table above: x: 1 2 3 4 f(x): 5 6 7 8 The range is:

a)

{5,6,7,8}

b)

{1,2,3,4}

c)

all real numbers

d)

{8}

13.

Given the table: x: -2 0 2 f(x): 10 8 6 Domain?

a)

A. {-2, 0, 2}

b)

B. {10, 8, 6}

c)

C. all real numbers

d)

D. x ≥ 0

14.

Given the table: x: -2 0 2 f(x): 10 8 6 Range?

a)

A. {10, 8, 6}

b)

B. {-2, 0, 2}

c)

C. y ≥ 0

d)

D. y ≤ 0

15.

Given the table: x: -3 -1 1 3 f(x): 2 4 6 8

a)

Domain: {-3, -1, 1, 3}, Range: {2, 4, 6, 8}

b)

Domain: {2, 4, 6, 8}, Range: {-3, -1, 1, 3}

c)

Domain: {-3, -1, 1}, Range: {2, 4, 6}

d)

Domain: {-3, 1, 3}, Range: {2, 6, 8}

16.

Domain?

a)

{-3, -1, 1, 3}

b)

{2, 4, 6, 8}

c)

all real numbers

d)

x > 0 only

17.

Range?

a)

{2,4,6,8}

b)

{-3,-1,1,3}

c)

y ≥ 0

d)

y ≤ 0

18.

Ordered Pairs 17. {(2,3), (4,5), (6,7)} Domain?

a)

A. {2,4,6}

b)

B. {3,5,7}

c)

C. all real numbers

d)

D. {3,5}

19.

Range?

a)

{3,5,7}

b)

{2,4,6}

c)

all real numbers

d)

{2}

20.

19. {(-1, 4), (0, 4), (2, 4)} Range?

a)

A. {4}

b)

B. {-1, 0, 2}

c)

C. all real numbers

d)

D. {0,4}

21.

20. {(1,2), (1,5), (1,8)} Domain?

a)

A. {1}

b)

B. {2,5,8}

c)

C. all real numbers

d)

D. {0,1}

22.

A graph has points at x = -3, -1, 0, and 4 only. Domain?

a)

{-3, -1, 0, 4}

b)

all real numbers

c)

{0,4}

d)

{-1,0}

23.

A graph has y-values 2, 3, and 5. Range?

a)

{2,3,5}

b)

all real numbers

c)

y > 5

d)

y < 2

24.

A graph shows points only: (1,5), (2,6), (3,7). Domain?

a)

{1,2,3}

b)

{5,6,7}

c)

all real numbers

d)

{6,7}

25.

Range?

a)

{5,6,7}

b)

{1,2,3}

c)

all real numbers

d)

y ≥ 0

26.

A graph has dots at (0,2), (2,4), (4,6), (6,8). Domain?

a)

{0,2,4,6}

b)

{2,4,6,8}

c)

all real numbers

d)

x ≥ 0

27.

Range?

a)

{2,4,6,8}

b)

{0,2,4,6}

c)

all real numbers

d)

y ≥ 0

28.

( f(x) = 2x ) Domain?

a)

A. all real numbers

b)

B. x ≥ 2

c)

C. x ≤ 2

d)

D. x ≠ 2

29.

( f(x) = 2x ) Range?

a)

A. all real numbers

b)

B. y ≥ 2

c)

C. y ≤ 2

d)

D. y ≠ 0

30.

( f(x) = 7 ) Domain?

a)

all real numbers

b)

x = 7 only

c)

x ≥ 7

d)

x ≠ 7

31.

30. ( f(x) = 7 ) Range?

a)

A. {7}

b)

B. all real numbers

c)

C. y ≥ 7

d)

D. y ≤ 7

32.

( f(x) = x - 1 ) Domain?

a)

A. all real numbers

b)

B. x ≥ 1

c)

C. x ≤ 1

d)

D. x ≠ 1

33.

32. ( f(x) = x - 1 ) Range?

4 lines
34.

( f(x) = sqrt{x + 4} ) Domain?

a)

x ≥ –4

b)

x ≤ –4

c)

x < 4

d)

all real numbers

35.

( f(x) = sqrt{x + 4} ) Range?

a)

y ≥ 0

b)

y ≤ 0

c)

y = –4

d)

all real numbers

36.

( f(x) = |x - 2| ) Domain?

a)

A. all real numbers

b)

B. x ≥ 2

c)

C. x ≤ 2

d)

D. x ≠ 2

37.

( f(x) = |x - 2| ) Range?

a)

y ≥ 0

b)

y ≤ 0

c)

y = 2

d)

all real numbers

38.

Input = number of apples, Output = total apples. Domain?

a)

whole numbers

b)

negative numbers

c)

fractions only

d)

x ≤ 0

39.

Same situation, range?

a)

whole numbers

b)

negative numbers

c)

y < 0

d)

all real numbers

40.

Input = number of days, Output = money earned at $10 per day. Domain?

a)

whole numbers

b)

negative numbers

c)

fractions

d)

x < 0

41.

Range?

a)

whole numbers

b)

negative numbers

c)

y < 0

d)

all real numbers

42.

41. {(0,0), (1,1), (2,2)} Domain?

a)

A. {0,1,2}

b)

B. {0,1,2}

c)

C. all real numbers

d)

D. {0,2}

43.

Range?

a)

{0,1,2}

b)

all real numbers

c)

y ≥ 0

d)

y = 1

44.

43. {(3,5), (3,7), (3,9)} Domain?

a)

A. {3}

b)

B. {5,7,9}

c)

C. all real numbers

d)

D. x ≠ 3

45.

Range?

a)

{5,7,9}

b)

{3}

c)

all real numbers

d)

y ≤ 0

46.

A horizontal line at y = 6. Range?

a)

{6}

b)

all real numbers

c)

y > 6

d)

y < 6

47.

For that line, domain?

a)

all real numbers

b)

x = 6 only

c)

x > 6

d)

x < 6

48.

A vertical line at x = -1. Domain?

a)

{-1}

b)

all real numbers

c)

x > -1

d)

x < -1

49.

For that vertical line, range?

a)

all real numbers

b)

y = -1

c)

y > -1

d)

y < -1

50.

If a graph has points (1,2), (2,2), (3,2), the range is:

a)

{2}

b)

{1,2,3}

c)

all real numbers

d)

y > 2

51.

If a function’s x-values are –5, –2, 0, and 7, the domain is:

a)

A. {–5, –2, 0, 7}

b)

B. all real numbers

c)

C. {–5,7}

d)

D. {0,1}

52.

Using Ordered Pairs: {(1,2), (2,3), (3,4)} Is this a function?

a)

Yes

b)

No

53.

Using Ordered Pairs: {(1,2), (1,3), (2,4)} Is this a function?

a)

Yes

b)

No

54.

Using Ordered Pairs: {(0,1), (1,1), (2,1)} Is this a function?

a)

Yes

b)

No

55.

Using Ordered Pairs: {(3,4), (4,4), (5,5), (3,5)} Is this a function?

a)

Yes

b)

No

56.

Using Ordered Pairs: {(–1,0), (0,0), (1,0)} Is this a function?

a)

Yes

b)

No

57.

Using Ordered Pairs: {(2,3), (3,2), (4,5), (5,6)} Is this a function?

a)

Yes

b)

No

58.

Using Ordered Pairs: {(1,1), (2,2), (1,2), (3,3)} Is this a function?

a)

Yes

b)

No

59.

Using Ordered Pairs: {(0,0), (1,1), (2,2), (3,3)} Is this a function?

a)

Yes

b)

No

60.

{(-2,5), (0,5), (2,5), (-2,6)}

a)

Yes

b)

No

61.

10. {(1,2), (2,3), (3,4), (4,5)}

a)

Yes

b)

No

62.

Is this a function?

a)

Yes

b)

No

63.

| x | 1 | 1 | 2 | 3 | | y | 2 | 3 | 4 | 5 |

a)

Yes

b)

No

64.

| x | 0 | 1 | 2 | 3 | | y | 1 | 1 | 1 | 1 |

a)

Yes

b)

No

65.

| x | -1 | 0 | 1 | 0 | | y | 2 | 3 | 4 | 5 |

a)

Yes

b)

No

66.

Is this relation a function?

a)

Yes

b)

No

67.

|x| 1 | 2 | 2 | 3 | |y| 5 | 6 | 7 | 8 | Is this relation a function?

a)

Yes

b)

No

68.

Is this relation a function?

a)

Yes

b)

No

69.

Is this relation a function?

a)

Yes

b)

No

70.

Is this relation a function?

a)

Yes

b)

No

71.

Is this relation a function?

a)

Yes

b)

No

72.

A straight line passing through all points.

a)

Function

b)

Not a function

73.

A vertical line at x = 2.

a)

Function

b)

Not a function

74.

A horizontal line at y = 5.

a)

Function

b)

Not a function

75.

A parabola opening upwards.

a)

Function

b)

Not a function

76.

A parabola opening sideways.

a)

Function

b)

Not a function

77.

A curve going through points (−1,2), (0,3), (1,4).

a)

Function

b)

Not a function

78.

A circle centered at the origin.

a)

Function

b)

Not a function

79.

An increasing straight line.

a)

Function

b)

Not a function

80.

A U-shaped graph that opens upward.

a)

Function

b)

Not a function

81.

30. A figure-eight graph.

a)

Function

b)

Not a function

82.

Graph shows points: (1,2), (2,3), (3,4).

a)

Function

b)

Not a function

83.

Graph shows points: (1,2), (1,3), (2,4).

a)

Function

b)

Not a function

84.

33. Table: x = {0,1,2}, y = {5,5,5}

a)

Function

b)

Not a function

85.

34. Table: x = {1,1,2}, y = {3,4,5}

a)

Function

b)

Not a function

86.

Graph: straight diagonal line passing through origin.

a)

Function

b)

Not a function

87.

Graph: vertical line at x = 0

a)

Function

b)

Not a function

88.

37. Points: {(–2,3),(0,3),(2,3)}

a)

Function

b)

Not a function

89.

38. Points: {(1,1),(1,2),(2,2)}

a)

Function

b)

Not a function

90.

39. Table: x = {1,2,3}, y = {2,3,4}

a)

Function

b)

Not a function

91.

Table: x = {1,1,1}, y = {2,2,2}

a)

Function

b)

Not a function

92.

A function that assigns each student their ID number.

a)

Function

b)

Not a function

93.

A function that assigns a room to each student, but some students share a room.

a)

Function

b)

Not a function

94.

A function giving the age of each student.

a)

Function

b)

Not a function

95.

A function assigning each person their favorite color. Some have multiple favorites.

a)

Function

b)

Not a function

96.

A function assigning each day of the week to a temperature.

a)

Function

b)

Not a function

97.

A function assigning each city to its mayor, only one mayor per city.

a)

Function

b)

Not a function

98.

A function assigning a number to a lottery ticket, but one ticket has two numbers.

a)

Function

b)

Not a function

99.

A function assigning each car a license plate number.

a)

Function

b)

Not a function

100.

A function assigning each house to the number of rooms in it.

a)

Function

b)

Not a function

101.

What is the DOMAIN of the function? ​ ​ (a)  

Choose from the below words
{2,3,4,5}
{2,3,4,5,8,9,10,11}
{8,9,10,11}
102.

What is the DOMAIN of the function? ​ ​ (a)  

Choose from the below words

{2,3,4,5}

{2,3,4,5,8,9,10,11}

{8,9,10,11}

103.

( f(x) = x^2 ) Domain?

a)

D. x ≠ 0

b)

C. x ≤ 0

c)

B. x ≥ 0

d)

A. all real numbers

104.

( f(x) = |x + 3| )
Range?

a)

y ≥ 0

b)

y = 3

c)

y ≤ 0

d)

all real numbers

105.

A graph shows points only: (0,1), (2,3), (4,5). Range?

a)

y ≥ 0

b)

{1,3,5}

c)

all real numbers

d)

{0,2,4}

106.

( f(x) = x^2 )
Range?

a)

all real numbers

b)

y ≥ 0

c)

y ≠ 0

d)

y ≤ 0

107.

Given the table:
x: 0 1 2 3
f(x): 4 5 6 7
Range?

a)

all real numbers

b)

{0,1,2,3}

c)

{4,5,6,7}

d)

y ≥ 4

108.

( f(x) = |x| )
Domain?

a)

x ≠ 0

b)

all real numbers

c)

x ≥ 0

d)

x ≤ 0

109.

Given the table:
x: 0 1 2
f(x): 3 5 7
What is the domain?

a)

{1, 2, 3}

b)

{0, 1, 2}

c)

all real numbers

d)

{3, 5, 7}

110.

( f(x) = 1/x )
Domain?

a)

all real numbers except 0

b)

x > 0 only

c)

x < 0 only

d)

x = 0 only

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