Exercise gives information that describes the relationship between two variables. You are to convert this information into a rule that relates the variables. The rule may take the form of an equation or some other form.
(See Example 1) Barber’s Tree Service charges $20 plus $15 per hour to trim trees. Write the rule relating the fee and hours worked using x for the number of hours worked and y for the fee. What do the numbers in the domain represent? What do the numbers in the range represent?
EXAMPLE 1
Mr. Riggs consults for a trailer manufacturing company. His fee is $300 for miscellaneous expenses plus $50 per hour. What is the domain of this function? The number of hours worked determines the fee, so the domain consists of the number of hours worked and the range consists of the fees charged. It makes sense to say that hours worked must be a positive number, and the minimum fee is $300. Thus, positive numbers make the domain, and numbers 300 or larger make the range. The rule that determines the fee that corresponds to the number of consulting hours is given by the formula
y = 50x + 300
where x represents the number of hours consulted and y represents the total fee in dollars. Note that the formula gives exactly one fee for each number of consulting hours. So, this determines a function where the domain consists of the set of numbers representing hours worked, and the range consists of the set of numbers representing the dollar amount of fees.
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