I cannot figure out the domain or the range.

Question

Thor has a job as a math tutor that paid $7 an hour and he made at most $210 every week.

If x is the hours he worked and y is the money he made in a week, write the domain and range of the function as compound inequalities

What I kept getting for Domain and Range was this...

Domain: 1≤x≤30

Range: 7≤y≤210

I am being told that both are wrong

Answer 1

The domain will be the values that make sense for x (number of hours worked). The tutor could work 0 hours (but for sure not a negative number of hours). If the tutor works more than 30 hours, then the earnings will be more than $210, so the most hours worked is 30.

So the domain is:

0 ≤ x ≤ 30

The range is the amount of money earned. If the tutor works 0 hours, then 0 dollars earned. If the tutor works 30 hours (the max) then the amount of money earned will be $210.

So the range is:

0 ≤ y ≤ 210