Deck 3: Functions

Question 1

Find the domain.

A)
B)
C)
D)
E)

Answer 1

Question 2

Determine the domain and the range.

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

Answer 2

domain: ; range:

Question 3

Let T(x) = 2x ² - 3x. Find (and simplify) the expression. T (x + 3) - T (x - 3)

A) 24x
B) 18x - 24
C) 24x - 18
D) 6x
E) 18x

Answer 3

24x - 18

Question 4

Find the domain.

A)
B)
C)
D)
E)

Question 5

Using the results in the table, graph the functions y = x ² , y = x ² - 2, and y = x ² + 2 on the same set of axes. x
X ²
X ² - 2
X ² + 2
0
0
-2
2 1
1
-1
3 2
4
2
6 3
9
7
11

A)
B)
C)
D)
E)

Question 6

Given that f and g are inverse functions. If f(7) = 12, what is g(12)?

A) 17
B) 12
C) 5
D) 4
E) 7

Question 7

Find the domain.

A)
B)
C)
D)
E)

Question 8

Find the domain.

A)
B)
C)
D)
E)

Question 9

Specify the domain and range of the given function. (The axes are marked in one-unit intervals.)

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

Question 10

A spherical weather balloon is being inflated in such a way that the radius is given by Assume that r is in meters and t is in seconds, with t = 0 corresponding to the time that inflation begins. If the volume of a sphere of radius r is given by find the time at which the volume of the balloon is

A) t = 5 sec
B) t = 6 sec
C) t = 3 sec
D) t = 2 sec
E) t = 1 sec

Question 11

Find the domain.

A)
B)
C)
D)
E)

Question 12

Sketch the graph.

A)
B)
C)
D)
E)

Question 13

Let f (x) = x ² . Find and simplify the indicated difference quotient.

A) y ² - h
B) 2y - h
C) 2y + h ²
D) 2y + h
E) y + h

Question 14

Set up a table and graph the function .

A)
B)
C)
D)
E)

Question 15

Let f(x) = x ³ + 2x + 1, and assume that the domain of f ^-1 is . Simplify .

A) t ³ + 3t + 5
B) (t + 5) ²
C)
D) t ² + 2t + 1
E) t + 5

Question 16

Set up a table and graph the function

A)
B)
C)
D)
E)

Question 17

Let T (x) = 4x ² - 3x. Find (and simplify) the expression. T (x + h) - T (x - h)

A) 16h - 3x
B) 16hx - 6h
C) 8x + 4h
D) 8x - 3h
E) 16hx + 3h

Question 18

Suppose that in a certain biology lab experiment, the number of bacteria is related to the temperature T of the environment by the function Here, N(T) represents the number of bacteria present when the temperature is T degrees Fahrenheit. Also, suppose that t hr after the experiment begins, the temperature is given by How many bacteria are present when t = 5 hr?

A) 300
B) 900
C) 1,200
D) 400
E) 600

Question 19

Determine the domain and the range.

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

Question 20

Assume that the accompanying viewing rectangle shows the essential features of the graph of f(x) = -x ³ + 4x+ 2. Use a graphing utility to estimate to the nearest hundredth the coordinates of the turning points. f(x) = -x ³ + 4x+ 2 [- 4, 4, 2] by [- 12, 12, 6]

A) (- 1.14, - 1.08),(1.14, 5.08)
B) (- 1.14, - 1.09),(1.14, 5.09)
C) (- 1.15, - 1.07),(1.15, 5.07)
D) (- 1.15, - 1.08),(1.15, 5.08)
E) (- 1.16, - 1.08),(1.16, 5.08)

Question 21

Let . Find g ^{- 1} (t).

A)
B)
C)
D)
E)

Question 22

Use a graphing utility to graph the function and then apply the horizontal line test to see whether the function is one-to-one. y = x ⁷ + 5x

A) True
B) False

Question 23

Let f(x) = 5x + 4. Find f ^{- 1} (x).

A)
B)
C)
D)
E)

Question 24

Assume that the domain of and is . Solve for t. .

A) t = - 6
B) t = 12
C) t = 7
D) t = - 7
E) t = -7