Deck 3: Functions

Question 1

Evaluate the function at the indicated value.
Find $f ( 6 )$ when $f ( x ) = \sqrt { x ^ { 2 } + 7 x }$ .

A) $\sqrt { 78 }$
B) $2 \sqrt { 14 }$
C) $\sqrt { 85 }$
D) $\sqrt { 43 }$

Answer 1

A

Question 2

Determine whether the relation represents a function. If it is a function, state the domain and range.

A)not a function
B)function
C)function domain: {3, 6, 9, 12} domain:{12, 24, 36, 48}
Range: {12, 24, 36, 48} range: {3, 6, 9, 12}

Answer 2

B

Question 3

Solve the variation problem.
$$y ^ { 2 } = 5 - x ^ { 2 }$$

A)function
B)not a function

Answer 3

B

Question 4

Determine whether the relation represents a function. If it is a function, state the domain and range.

A)not a function
B)function
C)function domain: {cat, dog} domain: {Alice, Brad, Carl}
Range: {Alice, Brad, Carl} range: {cat, dog}

Question 5

Determine whether the equation defines y as a function of x.
$$- 7 x + x ^ { 2 } - 48 = y$$

A)function
B)not a function

Question 6

Solve the variation problem.
$$y = x ^ { 2 }$$

A)function
B)not a function

Question 7

Solve the variation problem.
{(-2, 3), (-1, 0), (0, -1), (1, 0), (3, 8)}

A)function
B)function
C)not a function domain: {3, 0, -1, 8} domain: {-2, -1, 0, 1, 3}
Range: {-2, -1, 0, 1, 3} range: {3, 0, -1, 8}

Question 8

Solve the variation problem.
$$y ^ { 2 } + x = 8$$

A)function
B)not a function

Question 9

Evaluate the function at the indicated value.
Find $f ( x + h )$ when $f ( x ) = 3 x ^ { 2 } + 5 x + 2$

A) $3 x ^ { 2 } + 3 h ^ { 2 } + 5 x + 5 h + 2$
B) $3 \mathrm { x } ^ { 2 } + 3 \mathrm {~h} ^ { 2 } + 11 \mathrm { x } + 11 \mathrm {~h} + 2$
C) $3 x ^ { 2 } + 3 x h + 3 h ^ { 2 } + 5 x + 5 h + 2$
D) $3 x ^ { 2 } + 6 x h + 3 h ^ { 2 } + 5 x + 5 h + 2$

Question 10

Evaluate the function at the indicated value.
$$\text { Find } f ( 1 ) \text { when } f ( x ) = \frac { x ^ { 2 } - 4 } { x - 3 } \text {. }$$ A) $\frac { 3 } { 2 }$
B) $- \frac { 5 } { 2 }$
C) $- \frac { 3 } { 4 }$
D) $- \frac { 1 } { 2 }$

Question 11

Determine whether the relation represents a function. If it is a function, state the domain and range.
{(41, -2), (5, -1), (5, 0), (6, 1), (14, 3)}

A)not a function
B)function
C)function domain: {-2, -1, 0, 1, 3} domain: {41, 6, 5, 14}
Range: {41, 6, 5, 14} range: {-2, -1, 0, 1, 3}

Question 12

Determine whether the relation represents a function. If it is a function, state the domain and range.

A)function
B)function
C)not a function domain: {Alice, Brad, Carl} domain: {snake, cat, dog}
Range: {snake, cat, dog} range: {Alice, Brad, Carl}

Question 13

Evaluate the function at the indicated value.
Find $f ( x + 1 )$ when $f ( x ) = \frac { x ^ { 2 } - 4 } { x - 5 }$

A) $\frac { x ^ { 2 } - 3 } { x - 4 }$
B) $\frac { x ^ { 2 } + 2 x + 5 } { x - 4 }$
C) $\frac { x ^ { 2 } + 2 x - 3 } { x - 4 }$
D) $\frac { x ^ { 2 } + 2 x - 3 } { x + 6 }$

Question 14

Solve the variation problem.
$$y = 8 x ^ { 2 } - 8 x + 9$$

A)function
B)not a function

Question 15

Solve the variation problem.
x + 8y = 4

A)function
B)not a function

Question 16

Determine whether the relation represents a function. If it is a function, state the domain and range.
{(-2, 7), (1, 3), (3, 0), (8, -1)}

A)function
B)not a function
C)function domain: {7, 3, 0, -1} domain: {-2, 1, 3, 8}
Range: {-2, 1, 3, 8} range: {7, 3, 0, -1}

Question 17

Evaluate the function at the indicated value.
Find f(x - 1)when f(x)= 4x2 + 3x + 1. A) $4 x ^ { 2 } - 5 x + 8$
B) $- 5 x ^ { 2 } + 4 x + 2$
C) $4 x ^ { 2 } - 5 x + 2$
D) $4 x ^ { 2 } + 7 x + 8$

Question 18

Determine whether the equation defines y as a function of x.
$$\text { Find } f ( 1 ) \text { when } f ( x ) = x ^ { 2 } + 3 x + 2$$

A)2
B)-4
C)6
D)0

Question 19

Solve the variation problem.
$$x ^ { 2 } - 5 y ^ { 2 } = 1$$

A)function
B)not a function

Question 20

Solve the variation problem.
$$x = y ^ { 2 }$$

A)function
B)not a function

Question 21

Use the vertical line test to determine whether the graph represents a function.

A)function
B)not a function

Question 22

Evaluate the function at the indicated value.
Find $f ( x + h )$ when $f ( x ) = \frac { 8 x + 7 } { 9 x - 2 }$ .

A) $\frac { 8 x + 8 h + 7 } { 9 x - 2 }$
B) $\frac { 8 x + 15 h } { 9 x + 7 h }$
C) $\frac { 8 x + 8 h + 7 } { 9 x + 9 h - 2 }$
D) $\frac { 8 x + 7 h } { 9 x - 2 h }$

Question 23

Use the vertical line test to determine whether the graph represents a function.

A)function
B)not a function

Question 24

Use the vertical line test to determine whether the graph represents a function.

A)function
B)not a function

Question 25

Evaluate the function at the indicated value.

A)function
B)not a function

Question 26

Use the vertical line test to determine whether the graph represents a function.
$$h ( t ) = \frac { t - 4 } { t ^ { 3 } - 9 t }$$

A) rational function; $( - \infty , 0 ) \cup ( 0 , \infty )$
B) rational function; $( - \infty , 4 ) \cup ( 4 , \infty )$
C) rational function; $( \alpha , \infty )$
D) rational function; $( \infty , - 3 ) \cup ( - 3,0 ) \cup ( 0,3 ) \cup ( 3 , \infty )$

Question 27

Use the vertical line test to determine whether the graph represents a function.
f(x)= 5x - 1 A) polynomial function; $( - \infty , 0 ) \cup ( 0 , \infty )$
B) polynomial function; $( \infty , \infty )$
C) polynomial function; $( 0 , \infty )$
D) polynomial function; $[ 1 , \infty )$

Question 28

Use the vertical line test to determine whether the graph represents a function.

A)not a function
B)function

Question 29

Use the vertical line test to determine whether the graph represents a function.
$$f ( t ) = t ^ { 2 } + 2$$

A) polynomial function; $( \infty , \infty )$
B) polynomial function; $( - 2 , \infty )$
C) polynomial function; $( - \infty , - 2 ) \cup ( - 2 , \infty )$
D) polynomial function; $[ - 2 , \infty )$

Question 30

Use the vertical line test to determine whether the graph represents a function.

A)function
B)not a function

Question 31

Evaluate the function at the indicated value.
Find $\frac { f ( x + h ) - f ( x ) } { h }$ when $f ( x ) = x ^ { 2 } + 7 x + 4$

A) 1
B) $2 x + h + 4$
C) $2 x + h + 7$
D) $\frac { 2 x ^ { 2 } + 2 x + 2 x h + h ^ { 2 } + h + 8 } { h }$

Question 32

Use the vertical line test to determine whether the graph represents a function.
$$g ( x ) = \frac { 2 x } { x ^ { 2 } - 9 }$$

A) rational function; $( \infty , \infty )$
B) rational function; $( 9 , \infty )$
C) rational function; $( - \infty , 0 ) \cup ( 0 , \infty )$
D) rational function; $( \infty , - 3 ) \cup ( - 3,3 ) \cup ( 3 , \infty )$

Question 33

Evaluate the function at the indicated value.
Find $\frac { f ( x + h ) - f ( x ) } { h }$ when $f ( x ) = 4 x - 3$

A) $4 + \frac { - 6 } { h }$
B) $4 + \frac { 8 ( x - 3 ) } { h }$
C) 0
D) 4

Question 34

Use the vertical line test to determine whether the graph represents a function.

A)not a function
B)function

Question 35

Use the vertical line test to determine whether the graph represents a function.

A)not a function
B)function

Question 36

Use the vertical line test to determine whether the graph represents a function.
$$h ( x ) = \frac { x ^ { 2 } } { x ^ { 2 } + 8 }$$

A) rational function; $( \infty , \infty )$
B) rational function; $( - 8 , \infty )$
C) rational function; $( - \infty , 0 ) \cup ( 0 , \infty )$
D) rational function; $( - \infty , - 8 ) \cup ( - 8 , \infty )$

Question 37

Use the vertical line test to determine whether the graph represents a function.

A)not a function
B)function

Question 38

Use the vertical line test to determine whether the graph represents a function.

A)function
B)not a function

Question 39

Use the vertical line test to determine whether the graph represents a function.

A)not a function
B)function

Question 40

Use the vertical line test to determine whether the graph represents a function.

A)not a function
B)function

Question 41

Find the x-intercept(s)and the y-intercept of the function.
$$F ( x ) = 2 x ^ { 2 } - 10 x - 12$$

A) $( - 6,0 ) , ( - 1,0 ) , ( 0 , - 12 )$
B) $( - 6,0 ) , ( 1,0 ) , ( 0 , - 12 )$
C) $( 6,0 ) , ( 1,0 ) , ( 0 , - 12 )$
D) $( 6,0 ) , ( - 1,0 ) , ( 0 , - 12 )$

Question 42

Find the x-intercept(s)and the y-intercept of the function.
A) domain: $[ - 1 , \infty )$
range: $[ - 1 , \infty )$
B) domain: $( - \infty , - 1 )$ or $( - 1 , \infty )$
range: $( - \infty , - 1 )$ or $( - 1 , \infty )$
C) domain: $( - \infty , \infty )$
range: $[ - 1 , \infty )$
D) domain: $( - \infty , \infty )$
range: $( - \infty , \infty )$

Question 43

Use the graph to determine the function's domain and range. Write the domain and range in interval notation.
(- 2, - 1)

A)decreasing
B)constant
C)increasing

Question 44

Find the x-intercept(s)and the y-intercept of the function.
$h ( x ) = x ^ { 2 } - 3 x + 2$

A) $( - 1,0 ) , ( - 2,0 ) , ( 0,2 )$
B) $( 1,0 ) , ( - 2,0 ) , ( 0,2 )$
C) $( 1,0 ) , ( 2,0 ) , ( 0,2 )$
D) $( - 1,0 ) , ( 2,0 ) , ( 0,2 )$

Question 45

Find the x-intercept(s)and the y-intercept of the function.
A) domain: $( - \infty , - 3 ]$
range: $( - \infty , 2 ]$
B) domain: $( - \infty , \infty )$
range: $( - \infty , \infty )$
C) domain: $( - \infty , \infty )$
range: $( - \infty , 2 ]$
D) domain: $( - \infty , - 3 )$ or $( - 3 , \infty )$
range: $( - \infty , 2 )$ or $( 2 , \infty )$

Question 46

Use the graph to determine the function's domain and range. Write the domain and range in interval notation.
(-3, 0)

A)decreasing
B)increasing
C)constant

Question 47

Use the graph to determine the function's domain and range. Write the domain and range in interval notation.
(1, 2)

A)increasing
B)constant
C)decreasing

Question 48

Find the x-intercept(s)and the y-intercept of the function.
A) domain: $x = 1$
range: $( - \infty , \infty )$
B) domain: $x = 1$
range: $y = - 5$
C) domain: $( - \infty , \infty )$
range: $\mathrm { y } = - 5$
D) domain: $( - \infty , \infty )$
range: $( - \infty , \infty )$

Question 49

Use the graph to determine the function's domain and range. Write the domain and range in interval notation.
(0, 1)

A)increasing
B)decreasing
C)constant

Question 50

Use the vertical line test to determine whether the graph represents a function.
$$f ( x ) = \frac { 1 } { x ^ { 2 } + 6 x - 16 }$$ A) rational function; $( - \infty , - 8 ) \cup ( - 8,2 ) \cup ( 2 , \infty )$
B) rational function; $( - \infty , \infty )$
C) rational function; $( - \infty , 2 ) \cup ( 2 , \infty )$
D) rational function; $( - \infty , - 8 ) \cup ( - 8 , \infty )$

Question 51

Use the graph to determine the function's domain and range. Write the domain and range in interval notation.
$$\left( 1,\infty \right)$$

A)constant
B)decreasing
C)increasing

Question 52

Find the x-intercept(s)and the y-intercept of the function.
f(x)= -2

A)(-2, 0), no y-intercept
B)no x-intercept, (0, -2)
C)no x-intercept, no y-intercept
D)(-2, 0), (0, -2)

Question 53

Use the graph to determine the function's domain and range. Write the domain and range in interval notation.
(- 1, 0)

A)constant
B)decreasing
C)increasing

Question 54

Use the graph to determine the function's domain and range. Write the domain and range in interval notation.
A) domain: $[ 0,4 ]$
range: $( - \infty , \infty )$
B) domain: $( - \infty , \infty )$
range: $[ 0,4 ]$
C) domain: $( - \infty , \infty )$
range: $[ 3,4 ]$
D) domain: $[ 3,4 ]$
range: $( - \infty , \infty )$

Question 55

Classify the function as a polynomial function, rational function, or root function, and then find the domain. Write the domain in interval notation.
$$g ( x ) = 4 x + 9$$

A) $\left( 0 , \frac { 9 } { 4 } \right) , ( - 9,0 )$
B) $\left( \frac { 9 } { 4 } , 0 \right) , ( 0,9 )$
C) $\left( - \frac { 9 } { 4 } , 0 \right) , ( 0,9 )$
D) $\left( - \frac { 4 } { 9 } , 0 \right) , ( 0,9 )$

Question 56

Use the graph to determine the function's domain and range. Write the domain and range in interval notation.
(0, 3)

A)decreasing
B)constant
C)increasing

Question 57

Find the x-intercept(s)and the y-intercept of the function.
$$f ( x ) = x ^ { 3 } + 8 x ^ { 2 } - x - 8$$

A) $( - 1,0 ) , ( 1,0 ) , ( - 8,0 ) , ( 0 , - 8 )$
B) $( - 1,0 ) , ( 1,0 ) , ( 0,8 )$
C) $( - 1,0 ) , ( 1,0 ) , ( 0 , - 8 )$
D) $( - 1,0 ) , ( 1,0 ) , ( - 8,0 ) , ( 0,8 )$

Question 58

Find the x-intercept(s)and the y-intercept of the function.
A) domain: $[ 0 , \infty )$
range: $( - \infty , \infty )$
B) domain: $( - \infty , \infty )$
range: $[ - 3 , \infty )$
C) domain: $[ 0 , \infty )$
range: $[ 0 , \infty )$
D) domain: $[ 0 , \infty )$
range: $[ - 3 , \infty )$

Question 59

Classify the function as a polynomial function, rational function, or root function, and then find the domain. Write the domain in interval notation.
$$f ( x ) = \sqrt { 21 - x }$$

A) root function; $( \infty , \sqrt { 21 } ]$
B) root function; $( - \infty , \sqrt { 21 } ) \cup ( \sqrt { 21 } , \infty )$
C) root function; $( \infty , 21 ]$
D) root function; $( - \infty , 21 ) \cup ( 21 , \infty )$

Question 60

Use the graph to determine the function's domain and range. Write the domain and range in interval notation.
$$( 1 , \infty )$$

A)increasing
B)decreasing
C)constant

Question 61

Determine algebraically whether the function is even, odd, or neither.
Use the graph of f given below to find f(-12).

A)20
B)-8
C)0
D)-12

Question 62

The graph of a function is given. Decide whether it is even, odd, or neither.

A)even
B)odd
C)neither

Question 63

The graph of a function is given. Decide whether it is even, odd, or neither.
$$f ( x ) = \sqrt [ 3 ] { x }$$

A)even
B)odd
C)neither

Question 64

Determine algebraically whether the function is even, odd, or neither.
$$f ( x ) = \frac { x } { x ^ { 2 } + 5 }$$

A)even
B)odd
C)neither

Question 65

Determine algebraically whether the function is even, odd, or neither.
Is f(80)positive or negative?

A)negative
B)positive

Question 66

The graph of a function f is given. Use the graph to answer the question.

A)even
B)odd
C)neither

Question 67

The graph of a function f is given. Use the graph to answer the question.

A)even
B)odd
C)neither

Question 68

The graph of a function is given. Decide whether it is even, odd, or neither.
$$f ( x ) = - 8 x ^ { 2 } - 9$$

A)even
B)odd
C)neither

Question 69

The graph of a function is given. Decide whether it is even, odd, or neither.
$$f ( x ) = 9 x ^ { 3 } + 8$$

A)even
B)odd
C)neither

Question 70

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval.
(-1, 0)

A)decreasing
B)constant
C)increasing

Question 71

The graph of a function is given. Decide whether it is even, odd, or neither.

A)even
B)odd
C)neither

Question 72

The graph of a function is given. Decide whether it is even, odd, or neither.
$$f ( x ) = - 4 x ^ { 3 }$$

A)even
B)odd
C)neither

Question 73

The graph of a function is given. Decide whether it is even, odd, or neither.

A)even
B)odd
C)neither

Question 74

The graph of a function is given. Decide whether it is even, odd, or neither.
$$\sqrt [ 3 ] { 9 x ^ { 2 } + 8 }$$

A)even
B)odd
C)neither

Question 75

The graph of a function is given. Decide whether it is even, odd, or neither.
$$f ( x ) = \sqrt { x }$$

A)even
B)odd
C)neither

Question 76

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval.
Find the values of x, if any, at which f has a relative maximum. What are the relative maxima?

A)f has a relative maximum at x = 0; the relative maximum is 1
B)f has a relative maximum at x = -3 and 3; the relative maximum is 0
C)f has no relative maximum
D)f has a relative maximum at x = 3; the relative maximum is 1

Question 77

The graph of a function f is given. Use the graph to answer the question.
Find the values of x, if any, at which f has a relative minimum. What are the relative minima?

A)f has a relative minimum at x = 0; the relative minimum is 2
B)f has no relative minimum
C)f has a relative minimum at x = -2 and 2; the relative minimum is 0
D)f has a relative minimum at x = -2; the relative minimum is 0

Question 78

The graph of a function is given. Decide whether it is even, odd, or neither.

A)even
B)odd
C)neither

Question 79

The graph of a function is given. Decide whether it is even, odd, or neither.
$$f ( x ) = 3 x ^ { 4 } - x ^ { 2 }$$

A)even
B)odd
C)neither

Question 80

Determine algebraically whether the function is even, odd, or neither.
Is f(3)positive or negative?

A)negative
B)positive