Deck 3: 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

Find the domain of the function.

A)
B)
C) all real numbers
D) all real numbers
E) all real numbers

Answer 2

all real numbers

Question 3

Write the slope-intercept form of the equation of the line through the given point perpendicular to the given line. point: (-7, -8) line: -9x - 45y = 9

A)
B)
C)
D)
E)

Answer 3

Question 4

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

A)
B)
C)
D)
E)

Question 5

Does the table describe a function?

A) no
B) yes

Question 6

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

A)
B)
C)
D)
E)

Question 7

Does the table describe a function?

A) no
B) yes

Question 8

Does the table describe a function?

A) yes
B) no

Question 9

Does the table describe a function?

A) yes
B) no

Question 10

Find the zeroes of the functions algebraically.

A)
B)
C)
D)
E)

Question 11

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

A) 3.8
B)
C)
D)
E) -6.2

Question 12

Find the difference quotient and simplify your answer.

A)
B)
C)
D)
E)

Question 13

Find the value(s) of x for which f (x) = g (x).

A)
B)
C)
D)
E)

Question 14

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

A)
B)
C)
D)
E)

Question 15

Which set of ordered pairs represents a function from P to Q?

A)
B)
C)
D)
E)

Question 16

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

A)
B)
C)
D)
E)

Question 17

Gretel's Computer Repair Store purchases a network server for $1145. The machine has a useful life of 5 years after which time another one will have to be purchased. Assume depreciation of the machine is linear. Write a linear equation giving the value V of the network server during the 5 years it will be in use.

A)
B)
C)
D)
E)

Question 18

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. -2 2

A)
B)
C)
D)
E)

Question 19

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

A) domain: range:
B) domain: range:
C) domain: range:
D) domain: range:
E) domain: range:

Question 20

Use the Vertical Line Test to determine in which of the graphs y is not a function of x.

A) All of the choices (A, B, C, and D) represent functions.
B)
C)
D)
E)

Question 21

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

A)
B)
C)
D)
E)

Question 22

Write an equation for the function that is described by the following characteristics: the shape of , but moved eight units down, two units to the left, and then reflected in the x-axis

A)
B)
C)
D)
E)

Question 23

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 24

Which function does the graph represent?

A) g(x) =
B)
C) g(x) =
D) g(x) =
E) g(x) =

Question 25

Which graph represents the function? g(x) =

A)
B)
C)
D)
E)

Question 26

Use the position equation to write a function that represents the situation and give the average velocity of the object from time t₁ to time t₂. An object is thrown upward from a height of 174 feet at a velocity of 1 feet per second.
T₁ = 1, t₂ = 5

A)
B)
C)
D)
E)

Question 27

Use a graphing utility to graph the function and approximate (to two decimal places) any relative minimum or relative maximum values.

A) relative maximum: relative minimum:
B) relative maximum: relative minimum:
C) relative maximum: relative minimum:
D) relative maximum: relative minimum:
E) relative maximum: relative minimum:

Question 28

Graph the function and determine the interval(s) for which f (x) ³ 0.

A)
B)
C)
D)
E)

Question 29

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

A)
B)
C)
D)
E)

Question 30

Find .

A)
B)
C)
D)
E)

Question 31

Evaluate the indicated function for and . ( fg )(1)

A) 12
B) -32
C) -20
D) -16
E) -30

Question 32

Find the zeroes of the functions algebraically.

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

Question 33

Write the linear function f such that it has the indicated values.

A)
B)
C)
D)
E)

Question 34

Evaluate the function for the indicated values. f(x) = 4 x + 8 + 8
(i) (ii) (iii)

A)
B)
C)
D)
E)

Question 35

Which graph represents the function?

A)
B)
C)
D)
E)

Question 36

Describe the sequence of transformations from the related common function to g.

A) vertical shift 4 units up; then vertical shrink by a factor of 4
B) horizontal shift 4 units left; then vertical shrink by a factor of 4
C) horizontal shift 4 units right; then vertical stretch by a factor of 4
D) vertical shift 4 units down; then vertical shrink by a factor of 4
E) horizontal shift 4 units left; then vertical stretch by a factor of 4

Question 37

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

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

Question 38

Evaluate the indicated function for .

A)
B)
C)
D)
E)

Question 39

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

A) neither
B) even
C) odd

Question 40

Write the height h of the rectangle as a function of x.

A)
B)
C)
D)
E)

Question 41

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

A) 9
B) -1
C) 0
D) -4
E) -2

Question 42

Find .

A)
B)
C)
D)
E)

Question 43

Find the inverse function of f.

A)
B)
C)
D)
E)

Question 44

Find the inverse function of f.

A)
B)
C)
D)
E)

Question 45

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

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

Question 46

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

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

Question 47

Show algebraically that f and g are inverse functions.

Question 48

Graph the given function.

A)
B)
C)
D)
E)

Question 49

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

A)
B)
C)
D) undefined
E)

Question 50

The monthly cost C of running the machinery in a factory for t hours is given by The number of hours t needed to produce x products is given by . Find the equation representing the cost C of manufacturing x products.

A)
B)
C)
D)
E)

Question 51

Find .

A)
B)
C)
D)
E)

Question 52

Show algebraically that f and g are inverse functions.