Question

Goal: Find a reasonable domain and range for each function.

Question: a car can travel 32 miles for each gallon of gas. The function d(x) = 32x represents the distance d(x), in miles, that the car can travel with x gallons of gas. The car's fuel tank holds 17 gallons.

If you could also show work with this to show me how to do it later on, that would be awesome.

Answer 1

d(x) = 32x......ur range will be ur d(x) values and the domain will be ur x values.....where d(x) = total distance and x = gallons.
So we already know that ur car's fuel tank holds 17 gallons....therefore, ur domain has to be 17 gallons or less...but it cant be negative.
so ur domain is : 0 < = x < = 17

now for ur range....since the car only holds 17 gallons....d(x) = 32(17) = 544 miles....thats the farthest it can go...therefore it can go from 0 to 544 miles....so ur range is : 0 < = d(x) < = 544

or u could write it as : domain = (0,17) with 0 representing an empty tank and 17 representing a full tank.....and ur range = (0,544) with 0 representing 0 miles driven and 544 representing 544 miles driven