﻿ Function Worksheets - Page 7 | Problems & Solutions

# Function Worksheets - Page 7

Function Worksheets
• Page 7
61.
Find the range for the function.
$f$($x$) = $x$ + 2 if $x$ < 0
= $x$ - 2 if $x$ > 0
 a. all negative integers b. all positive integers c. all real numbers d. all natural numbers

62.
Find the domain for the values shown in the table.
 $x$ $y$ - 3 9 - 2 4 - 1 1 0 0 1 1
 a. {- 3, - 2,- 1, 0, 1} b. {0, 1, 9, 4} c. all real numbers d. all integers

63.
Which of the following tables represents a function?

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

64.
Which of the following represents a function?

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

65.
Which of the following is not a function?
 a. {(1, 2), (2, 1), (3, 2), (1, 1)} b. {(1, 1), (2, 2), (3, 1), (4, 3)} c. {(4, 1), (3, 2), (1, 3), (2, 4)} d. {(5, 1), (4, 2), (3, 3), (2, 2)}

66.
The amount spent by Chris on a birthday party is a function of number of his friends whom he invited. Which of the following is a dependent variable?
 a. Chris′s age b. number of members in Chris′s family c. number of friends Chris invited d. amount spent by Chris on the party

#### Solution:

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

From the given function, independent variable is the number of friends and the dependent variable is amount Chris spent.

Among the choices, "amount spent by Chris on the party" is dependent variable.

67.
Find the range of $f$($x$) = 7$x$ + 2, if the domain is 2.
 a. 16 b. - 16 c. -17 d. 14

#### Solution:

f(x) = 7x + 2
[Given function.]

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

f(2) = 7(2) + 2 = 16
[Substitute 2 for x in f(x) and simplify.]

Therefore, the range of the function is 16.

68.
Determine whether the relation is a function. Find its domain and range, if it is a function.

 a. It is a function; domain is 3, 5, 7, 9, 11 and range is 1, 2, 3, 4. b. It is a function; domain is 0 and range is 3. c. It is a function; domain is 0, 1, 2, 3, 4 and range is 3, 5, 7, 9, 11. d. It is not a function.

#### Solution:

In the given relation, for each input there is exactly one output.

So, the relation is a function.

The domain of the function is 0, 1, 2, 3, 4.
[The collection of all input values is the domain.]

The range of the function is 3, 5, 7, 9, 11.
[The collection of all output values is the range.]

69.
Find the range of the set.
{(- 3, 6), (4, 2), (7, 25), (8, 28)}
 a. {- 3, 4, 7, 8} b. {- 3, 6, 4, 2, 7, 25, 8} c. {4, 2, 7, 8} d. {2, 6, 25, 28}

#### Solution:

The set of second coordinates of all the ordered pairs of a relation is known as the range.

The second coordinates are 6, 2, 25 and 28.

So, the range of the given set is {2, 6, 25, 28}.

70.
Write the domain and range of the relation shown in the table.

 a. Domain is {- 2, - 4, 6, 8, 9}, Range is {- 3, 4, 5, - 7, 4} b. Domain is {- 3, 4, 5, - 7, 4}, Range is {- 2, - 4, 6, 8, 9} c. Domain is {- 2, - 4}, Range is {- 3, - 7} d. Domain is {6, 8, 9}, Range is {- 3, - 7}

#### Solution:

The set of first coordinates of all the ordered pairs of a relation is known as the domain.

The first coordinates are - 2, - 4, 6, 8 and 9.

So, the domain of the given relation is {- 2, - 4, 6, 8, 9}.

The set of second coordinates of all the ordered pairs of a relation is known as the range.

The second coordinates are - 3, 4, 5, - 7 and 4.

So, the range of the given relation is {- 3, 4, 5, - 7, 4}.