John's old '87 Lebaron has a 15 gal gas tank and gets 23 mpg. The number of miles he can drive is a function of how much gas is in the tank. Require (a) write this relationship in equation form and (b) determine the domain and range of the function in the context.
Solution
Let x = gallons of gas in the tank
y = number of miles
Therefore, y = 23x which is bounded by the following ranges:
- 0 <= x <= 23 for the amount of gas in the tank can not go below 0 and above 15 gallons
- 0 <= y <= 345 for the number of miles John can travel can not go below 0 and above 345 miles (23 mpg multiplied by 14 gallons)
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The explanation for number one is correct, however, the Domain is not correct. It should be 0<=x<=15, once again, because the amount of gas can't be less than 0, nor could it exceed 15.
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