Acompany rents moving vans for a charge of $30 plus $0.50 per mile. the company only allows its vans to be user for "in-town" moves, with total mileage limited to 100 miles. the total rental cost, c(m), (in dollars) is a function of the distance m (in miles) that the van is driven. state a rule for the function, graph the function, and state its domain and range

The function would be:

Because the rent cost $30 initially, and then $0.50 per mile additionally. So, the $30 is a constant, and the $0.50 is variable, so it has to be with the independent variable.

However, we need to set one restriction, because the problem says that the total mileage is limited to 100 miles. This means that   cannot be more than 100 miles, or it could be equal or less than 100 miles.

So, this restriction would be:

Also, if miles are restricted, then, costs are also restricted to less than 100 miles:

Therefore, the cost is not higher than $80:

Therefore, the function and restrictions would be:

the distance between point a and point b is 6 units