﻿ Function Worksheets - Page 8 | Problems & Solutions

# Function Worksheets - Page 8

Function Worksheets
• Page 8
71.
Find the range of $f$($x$) = 6$x$ - 1, if the domain is - 2.
 a. - 13 b. 3 c. - 12 d. 13

#### Solution:

f(x) = 6x - 1
[Given function.]

The range of the function can be determined by sustituting the values in the domain of the function.

f(- 2) = 6(- 2) - 1 = - 13
[Substitute - 2 for x in f(x) and simplify.]

Therefore, the range of the function is - 13.

72.
The radius of a circle is $r$. If the area of the circle is given as A = $\pi$$r$2, then which of the following is true?
 a. $r$ is a dependent variable b. A is an independent variable c. A is a dependent variable d. $\pi$ is a dependent variable

#### Solution:

Independent variable is the input and the dependent variable is the output of the situation.

From the given function, independent variable is r and the dependent variable is A.
[r is the input and A is the output.]

Therefore, the statement 'A is a dependent variable' is true.

73.
A function is described by the equation $f$($x$) = 2$x$ + 1. The replacement set for the independent variable is {0, 2, 3, 4}. Which of the following is contained in the corresponding set for the dependent variable?
 a. 9 b. 2 c. 3 d. 15

#### Solution:

Independent variable is the input and the dependent variable is the output of the function.

Substitute the values of x and find the corresponding values of f(x).

For x = 0, f(0) = 2(0) + 1 = 1
[Substitute x = 0 in f(x) = 2x + 1.]

For x = 2, f(2) = 2(2) + 1 = 5
[Substitute x = 2 in f(x) = 2x + 1.]

For x = 3, f(3) = 2(3) + 1 = 7
[Substitute x = 3 in f(x) = 2x + 1.]

For x = 4, f(4) = 2(4) + 1 = 9
[Substitute x = 4 in f(x) = 2x + 1.]

The set for the dependent variable is {1, 5, 7, 9}.

Among the choices, the value 9 is in the dependent variable set.

74.
Which of the following tables does not represent a function?

 a. Table 1 b. Table 4 c. Table 3 d. Table 2

#### Solution:

Table 1, Table 2, Table 3 represent a function, since there is exactly one output for each input.

In Table 4, the input value 2 has two output values 10 and 14.

Table 4 does not represent a function.

75.
Which of the function tables represents the function $f$($x$) = 5$x$ + 2, for $x$ = 0, 1, 2, 3, and 4 as domain?

 a. Table 4 b. Table 1 c. Table 3 d. Table 2

#### Solution:

f(x) = 5x + 2
[Original function.]

x = 0, f(0) = 5(0) + 2 = 2
[Substitute the domain values in the function.]

x = 1, f(1) = 5(1) + 2 = 7

x = 2, f(2) = 5(2) + 2 = 12

x = 3, f(3) = 5(3) + 2 = 17

x = 4, f(4) = 5(4) + 2 = 22

The values of x and f(x) matches with the Table 2.

So, Table 2 represents the given function.

76.
Which table represents a function?

 a. Table 1 b. Table 2 c. Table 4 d. Table 3

#### Solution:

A relation is a function if it has exactly one output for each input.

In Table 1, the input value 1 has two output values 15 and 60.

In Table 2, the input value 2 has two output values 30 and 45.

In Table 3, the input value 4 has two output values 15 and 60.

Table 4 represents a function, since there is exactly one output for each input.

So, Table 4 represents a function.

77.
The side of a cube is $a$. If the volume of the cube is given as V = $a$3, then which of the following is true?
 a. $a$2 is a dependent variable b. $a$ is a dependent variable c. V is a dependent variable d. V is an independent variable

#### Solution:

Independent variable is the input and the dependent variable is the output of the situation.

From the given function, independent variable is a and the dependent variable is V.
[a is the input and V is the output.]

Therefore, the statement 'V is a dependent variable' is true.

78.
The side of a square is $a$. If the perimeter of the square is given as P = 4$a$, then which of the following is true?
 a. $a$ is a dependent variable b. P is an independent variable c. 4 is a dependent variable d. $a$ is an independent variable

#### Solution:

Independent variable is the input and the dependent variable is the output of the situation.

From the given function, independent variable is a and the dependent variable is P.
[a is the input and P is the output.]

Therefore, the statement 'a is an independent variable' is true.

79.
A function is described by the equation $f$($x$) = $x$ + 1. The replacement set for the independent variable is {1, 3, 5, 7}. Which of the following is not contained in the corresponding set for the dependent variable?
 a. 6 b. 10 c. 8 d. 4

#### Solution:

Independent variable is the input and the dependent variable is the output of the function.

Substitute the values of x and find the corresponding values of f(x).

For x = 1, f(1) = 1 + 1 = 2
[Substitute x = 1 in f(x) = x + 1.]

For x = 3, f(3) = 3 + 1 = 4
[Substitute x = 3 in f(x) = x + 1.]

For x = 5, f(5) = 5 + 1 = 6
[Substitute x = 5 in f(x) = x + 1.]

For x = 7, f(7) = 7 + 1 = 8
[Substitute x = 7 in f(x) = x + 1.]

The set for the dependent variable is {2, 4, 6, 8}.

Among the choices, the value 10 is not in the dependent variable set.

80.
Find the distances traveled by Holly and Rebecca in 2, 6 and 11 hours, if they traveled at a steady rate of 30 miles per hour.
 a. 70, 160 and 345 miles b. 60, 110 and 30 miles c. 60, 180 and 330 miles d. 80, 182 and 318 miles

#### Solution:

Distance = speed x time
[Write Distance in terms of speed and time.]

d = 30 x 2
[Distance traveled in 2 hours.]

= 60
[Multiply.]

d = 30 x 6
[Distance traveled in 6 hours.]

= 180
[Multiply.]

d = 30 x 11
[Distance traveled in 30 hours.]

= 330
[Multiply.]

The distances traveled by Holly and Rebecca in 2, 6 and 11 hours are 60, 180 and 330 miles respectively.