Answer:
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
Step-by-step explanation:
A function is a relation where each input value has only one output value
a. The given data are presented as follows
[tex]\begin{array}{cc}Width \, (m)&Area \, (m^2)\\1&9\\5&50\\10&150\\11&176\\14&266\end{array}[/tex]
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
[tex]\begin{array}{cc}Hours \ worked &Salary\\0&0\\10&\$300\\20&\$600\\30&\$900\\40&\$1200\end{array}[/tex]
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
[tex]\begin{array}{cc}Height \, (cm)&Age\, (years)\\160&20\\160&25\\160&30\\160&35\\160&40\end{array}[/tex]
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