Let's write the function first and use it to determine the domain and range.
Writing the Function
To write a function for this situation, we will express each piece of given information algebraically. From there we will combine the parts to form the function.
Verbal Expression
Algebraic Expression
Increase in earnings per hour
8.5
Increase in earnings after h hours
8.5 h
Earnings after h hours
f( h)= 8.5 h
Since earnings depends on the number of hours Takumi works, we can say that the number of hours is the independent variable and will represent the domain. Earnings is the dependent variable, so this will represent the range.
Determining Domain and Range
We are told that Takumi works no more than 5 hours a day, so a reasonable domain would be integers from 1 to 5. Let's determine the range using a table of values.
Function
Number of Hours
Calculation
Temperature
f(h)=8.5h
1
f( 1)=8.5( 1)
$8.5
f(h)=8.5h
2
f( 2)=8.5( 2)
$17
f(h)=8.5h
3
f( 3)=8.5( 3)
$25.5
f(h)=8.5h
4
f( 4)=8.5( 4)
$34
f(h)=8.5h
5
f( 5)=8.5( 5)
$42.5
Thus, we can write the domain and range as the following.
Domain:&{1,2,3,4,5}
Range:&{$8.5,$17,$25.5,$34,$42.5}
