Motorists often complain about rising gas prices. Some motorists purchase fuel efficient vehicles and participate in trip reduction plans, such as carpooling and using alternative transportation. Other drivers try to drive only when necessary.
Suppose you are at the gas station filling your tank with gas. The function C(g) represents the cost C of filling up the gas tank with g gallons. Given the equation:C(g)= 3.03(g).
For the average motorist, name one value for g that would be inappropriate for this function’s purpose. Explain why you chose the number you did.
If you were to graph C(g), what would be an appropriate domain? Range? Explain your reasoning.
Would you fit a billion gallons of gas in your tank? Could you afford to?
Would you stop to buy 1 thousandth of a gallon?
The appropriate domain will be somewhere inbetween. You figure out what, based on your own good sense.
Given your domain, the range easily falls into place.
An inappropriate value for the purpose of this function would be a negative value for g. This is because it is not possible to have a negative number of gallons of gas. In this context, the function C(g) represents the cost of filling up the gas tank with g gallons, and it would make no sense to calculate the cost for a negative number of gallons.
In terms of the domain and range of the function C(g), the domain would be all non-negative real numbers, including zero. This is because it is possible to fill the gas tank with 0 gallons, meaning no gas is purchased. It also includes all positive values, representing any amount of gas greater than zero that can be purchased.
The range of the function C(g) would be all non-negative real numbers, including zero. This is because the cost of filling up the gas tank will always be a non-negative value or zero. It is not possible to have a negative cost for filling up the gas tank. The range would include all values greater than or equal to zero, representing the possible costs of filling the tank.