QuestionJohn earns per hour for up to 40 hours weekly. Explain and state the domain & range.
Studdy Solution
STEP 1
Assumptions1. John gets paid (h) =8.5h(25) =212.5$ and find the domain and range of the function.
STEP 2
The function represents John's weekly pay. Here, is the number of hours John works in a week and is the amount he gets paid for those hours.
STEP 3
To interpret , we plug in into the function.
STEP 4
Calculate the value of .
STEP 5
The interpretation of is that John earns $212.5 when he works for25 hours in a week.
STEP 6
Now, let's find the domain of the function. The domain of a function is the set of all possible input values (in this case, the number of hours John can work in a week).
Since John can work for a maximum of40 hours in a week, the domain of the function is .
STEP 7
Now, let's find the range of the function. The range of a function is the set of all possible output values (in this case, the amount John can earn in a week).
Since John earns 0 (if he doesn't work at all) and the maximum he can earn is (if he works the maximum number of hours).
STEP 8
Calculate the maximum amount John can earn in a week.
STEP 9
Calculate the value of the maximum earnings.
STEP 10
So, the range of the function is .
In conclusion, the interpretation of is that John earns 0 \leq h \leq400 \leq(h) \leq340$.
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