Answer
A. c is the independent variable and p is the dependent variable.
B. Yes, there is a function between the relationship of c and p as for each number of cars washed, there is a certain profit, p, that they can make.
C. P(c)=5c-34
D. The domain for this function is 0$\leq$c$\leq$40, and the range which is profit is from 0$\leq$p$\leq$166
Work Step by Step
A. c is the independent variable and p is the dependent variable, because the profit to be made, depends on the number of cars that are washed.
B. Yes, there is a function between the relationship of c and p as for each number of cars washed, there is a certain profit, p, that they can make.
C. P(c)=5c-34
This is the function rule for this relationship because they have to subtract 34 from the money raised by washing cars as they invest 34 before making any profit. Also they have to multiply 5 by c because they make 5 for every car that is washed which makes 5 the slope of the function.
D. The domain for this function is 0$\leq$c$\leq$40, because they can wash 0 cars and a max of 40 cars with the soap they bought. The range which is profit is from 0$\leq$p$\leq$166. the range is this because the minimum profit they can make is 0 dollars and the Max they can make is 166 which is when c=40 as it is the max number of cars they can wash. p(40)=5(40)-34= 200-34=$166.
