We know that:
Harrison gets $9.50 per hour of work.
He can work a maximum of 15 hours per week.
He needs to earn a minimum of $28.50 per week.
A) We want a function f(h) that tells how much he wins in a week if he works h hours.
So we know that he gets $9.50 per hour of work, then if he works h hours, he gets h times $9.50, then we can just write:
f(h) = $9.50×h
B) First remember that the domain is the set of possible values of h, and the range is the set of possible values of f(h).
We know that the maximum value of h is 15, to find the minimum value of h we need to use the other restriction, that he needs to win at least $28.50, then we need to solve:
$9.50×h = $28.50
h = ($28.50)/($9.50) = 3
Then we can conclude that the domain is:
D = [3, 15]
To find the range, we just need to evaluate the function in the minimum and maximum values of the domain:
f(3) = $28.50
f(15) = $142.50
Then the range is:
R = [$28.50, $142.50]
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