Deck 2: Functions and Their Graphs

Question 1

Find all real values of x such that f (x) = 0.

A)
B)
C)
D)
E)

Answer 1

Question 2

Which equation does not represent y as a function of x?

A)9y = 6
B)-2x = y
C)-4x + y = -8
D)-9x² + 8y = 4
E)-2y² - 6x = 1

Answer 2

-2y² - 6x = 1

Question 3

Find the zeroes of the functions algebraically.

A)x = 7, x = -8,
B)x = 7, x = -8
C)
D)x = -7, x = 8
E)x = -7, x = 8,

Answer 3

x = -7, x = 8

Question 4

Find the domain of the function.

A)-9 $\le$ t $\le$ 9
B)t $\le$ -9 or t $\ge$ 9
C)t $\ge$ 0
D)t $\le$ 9
E)all real numbers

Question 5

Use the graph of the function to find the domain and range of f.

A)
B)
C)
D)
E)

Question 6

Use a graphing utility to graph the function and find the zeroes of the function.

A)
B)
C)
D)
E)no real zeroes

Question 7

Find all real values of x such that f (x) = 0.

A)
B)
C)
D)
E)

Question 8

A rectangle is bounded by the x-axis and the semicircle (see figure). Write the area A of the rectangle as a function of x and determine the domain of the function. -5 5

A) , -5 $\le$ x $\le$ 5
B) , x $\ge$ 0
C) , -5 $\le$ x $\le$ 5
D) , all real numbers
E) , x $\ge$ 0

Question 9

Find the zeroes of the functions algebraically.

A)
B)
C)
D)
E)no real zeroes

Question 10

Find the value(s) of x for which f (x) = g (x).f (x) = x² - 4x - 31 g (x) = -3x - 1

A)-31, -27,
B)-31, -4,
C)6, -5
D)-6, 5
E)35,

Question 11

Find the domain of the function.

A)all real numbers
B)all real numbers ,
C)all real numbers
D)s = -1, s = 0
E)s = -1

Question 12

Does the table describe a function?

A)yes
B)no

Question 13

Does the table describe a function?

A)yes
B)no

Question 14

Evaluate the function at the specified value of the independent variable and simplify.

A)
B)
C)
D)
E)

Question 15

Does the table describe a function?

A)yes
B)no

Question 16

Find the difference quotient and simplify your answer.f (x) = 8x² - 7x, , h $\neq$ 0

A)1 + h
B)
C)
D)-7 + 8h
E)57 + 8h

Question 17

Which set of ordered pairs represents a function from P to Q?P = {2, 4, 6, 8} Q = {-5, -3, -1}

A){(2, -5), (4, -3), (4, -1), (6, -3), (8, -5)}
B){(6, -5), (6, -3), (6, -1)}
C){(6, -3), (4, -5), (2, -3), (4, -1), (6, -5)}
D){(4, -3), (6, -1), (8, -3)}
E){(2, -1), (6, -3), (2, -5), (6, -1)}

Question 18

Evaluate the function at the specified value of the independent variable and simplify. f (w - 5)

A)
B)
C)
D)
E)

Question 19

Does the table describe a function?

A)no
B)yes

Question 20

Evaluate the function at the specified value of the independent variable and simplify.q (t) = -9t - 1q (1.6)

A)-14.4t + 9
B)-13.4
C)-15.4
D)1.6t - 1
E)1.6t + 1

Question 21

Find ( f / g )(x).

A)
B)
C)
D)
E)

Question 22

Find f (x) = -3x - 7 g (x) = x + 4

A) -3x - 19
B) -3x - 3
C) -3x² - 19x - 28
D) -4x - 11
E) -4x - 3

Question 23

Evaluate the indicated function for f (x) = x² - 8 and g (x) = x + 2.( fg )(3)

A)5
B)-85
C)11
D)1
E)-31

Question 24

Determine whether the function is even, odd, or neither.

A)
B)
C)

Question 25

Use the graph of to write an equation for the function whose graph is shown.

A)
B)
C)
D)
E)

Question 26

Use the graphs of f and g to evaluate the function.

A)0
B)4
C)9
D)-4
E)-1

Question 27

Find f (x) = x + 7 g (x) = x²

A) x² + 7
B) x² - 49
C) x² + 49
D) x² + 7x + 49
E) x² + 14x + 49

Question 28

Find

A)
B)
C)
D)
E)

Question 29

Find the inverse function of

A)
B)
C)
D)
E)

Question 30

Find ( f - g )(x).

A)
B)
C)
D)
E)

Question 31

Graph the function and determine the interval(s) for which f (x) $\ge$ 0.f (x) = -x² - 2x

A)
B)
C)
D)
E){-2}

Question 32

Use a graphing utility to graph the function and approximate (to two decimal places) any relative minimum or relative maximum values.f (x) = x³ + x² - 3x + 2

A)relative maximum: (-1.39, 5.42)relative minimum: (0.72, 0.73)
B)relative maximum: (0.72, 0.73)relative minimum: (-1.39, 5.42)
C)relative maximum: (5.42, -1.39)relative minimum: (0.73, 0.72)
D)relative maximum: (0.73, 0.72)relative minimum: (5.42, -1.39)
E)relative maximum: (0.73, 0.73)relative minimum: (5.42, 174.00)

Question 33

Find the inverse function of f.

A)
B)
C)
D)
E)

Question 34

Use a graphing utility to graph the function and visually determine the intervals over which the function is increasing, decreasing, or constant.

A)
B)
C)
D)
E)

Question 35

Evaluate the indicated function for f (x) = x² + 6 and g (x) = x - 3.( f-g )(t - 6)

A)t² - 13t + 51
B)t² - 13t + 45
C)t² - 11t + 51
D)t² - 11t + 45
E)t² - t + 51

Question 36

Find f (x) = x + 4

A)
B)
C)
D)
E)

Question 37

Find ( f + g)(x).f (x) = 6x² + 6x + 1g(x) = -4x² - 4x + 3

A)( f + g)(x) = 10x⁴ + 10x² - 2
B)( f + g)(x) = 2x⁴ + 2x² + 4
C)( f + g)(x) = 10x² + 10x - 2
D)( f + g)(x) = 2x² + 2x + 4
E)( f + g)(x) = -2x² - 2x - 4

Question 38

Find ( fg )(x).

A)
B)
C)
D)
E)

Question 39

Find the inverse function of

A) ,
B) ,
C) ,
D) ,
E) ,

Question 40

Determine the intervals over which the function is increasing, decreasing, or constant.

A)
B)
C)
D)
E)

Question 41

Find the inverse function of f.

A)
B)
C)
D)
E)

Question 42

Determine whether the variation model below is of the form or .

A)
B)

Question 43

Use the functions given by and to find the indicated value.

A)
B)
C)
D)
E)undefined

Question 44

Assume that y is directly proportional to x. If and , determine a linear model that relates y and x.

A)
B)
C)
D)
E)

Question 45

The simple interest on an investment is directly proportional to the amount of the investment. By investing $7750 in a certain certificate of deposit, you obtained an interest payment of $201.50 after 1 year. Determine a mathematical model that gives the interest, I , for this CD after 1 year in terms of the amount invested, P.

A)
B)
C)
D)
E)

Question 46

Determine whether the variation model below is of the form or .

A)
B)

Question 47

Determine whether the function has an inverse function. If it does, find the inverse function.

A)No inverse function exists.
B)
C)
D)
E)

Question 48

Determine whether the function has an inverse function. If it does, find the inverse function.

A)No inverse function exists.
B)
C)
D)
E)

Question 49

The sales tax on an item with a retail price of $932 is $74.56. Create a variational model that gives the retail price, y, in terms of the sales tax, x, and use it to determine the retail price of an item that has a sales tax of $88.54.

A)
B)
C)
D)
E)