b The relationship between p and c is a function because there is a unique amount of earned profit p for each number of cars c that are washed. It is not possible to make two different profits out of the same number of washed cars.
c To write an equation for this relationship, we will translate the verbal expressions into algebraic expressions. Let's make a table for this purpose.
Verbal Expression
Algebraic Expression
Amount earned for one car
$5
Number of cars washed
c
Amount earned for c numbers of cars being washed
5c
Cost of soap
$34
Amount earned from washing cars minus the initial cost of the soap
5c- 34
Therefore, the equation for the profit p can be written as p= 5c- 34.
d Since the group can wash at least 0 cars and at most 40 cars using their purchased soap, the domain consists of all integers between 0 and 40 inclusive.
0 ≤ c ≤ 40
The range can be found by substituting the limits of the domain into the function. Let's first find the lower limit of the range.
If the group washes no cars, the loss will be $ 34. This means there is $0 in profit, so 0 will be our lower limit. Let's now find the upper limit for the range.
