Question

Determine whether each relation is a function. If so, provide the domain and range.

a. Width versus area.

Width (m) | Area (m2)

1 6

5 50

10 150

11 176

14 266

Function?


If so,

Domain =


Range =



b. Hours worked versus salary.

Hours Worked | Salary

0 0

10 $300

20 $600

30 $900

40 $1200

Function?


If so,

Domain =


Range =



c. Height versus age.

Height (cm) | Age (years)

160 20

160 25

160 30

160 35

160 40

160 45

160 50


Function?


If so,

Domain =


Range =

Answer 1

a. Function: Yes

Domain = 1, 5, 10, 11, 14

Range = 6, 50, 150, 176, 266

b. Function: Yes

Domain = All positive integers

Range = All positive integers

c. Function: The relation is not a function

Explanation:

A function is a relation where each input value has only one output value

a. The given data are presented as follows

`\begin{array}{cc}Width \, (m)&Area \, (m^2)\\1&9\\5&50\\10&150\\11&176\\14&266\end{array}`

For each value of the input variable, the width, there is exactly one out put variable, therefore, the relation is a function

Function; Yes

The domain, the input values, includes; 1, 5, 10, 11, 14

The range, the output, values, includes; 6, 50, 150, 176, 266

b. Hours worked versus salary

`\begin{array}{cc}Hours \ worked &Salary\\0&0\\10&\$300\\20&\$600\\30&\$900\\40&\$1200\end{array}`

For each value of the input variable, hours worked, there is exactly one out put variable, therefore, the relation is a function with the following equation;

Salary = $30 × Hours worked

Function; Yes

The domain, the input values, includes; All positive integers

The range, the output, values, includes; All positive integers

c. Height versus age

`\begin{array}{cc}Height \, (cm)&Age\, (years)\\160&20\\160&25\\160&30\\160&35\\160&40\end{array}`

For each value of the input variable, the height, there are more than one out put variable, the age, therefore, the relation is not a function

Function; No