Question

Kirsten is driving to a city that is 400 miles away. When Kirsten left home, she had 15 gallons of gas in her car. Assume that her car gets 25 miles per gallon of gas. Define a function f so that f(x) is the amount of gas left in her car after she has driven x miles from home. What are intercepts for that function. What do they represent.

Answer 1

The equation that gives us the amount of gas left in her car, given the driven miles, is

`f(x)=15-(x)/(25)`

Notice that when x=25, there will remain 14 gallons of gas in the tank.

The x-intercept is

`\begin{gathered} f(x)=0 \\ \Rightarrow0=15-(x)/(25) \\ \Rightarrow x=15\cdot25=375 \end{gathered}`

(375,0). This is the maximum distance one can drive when the amount of gas in the tank reaches zero gallons.

On the other hand, the y-intercept is

`\begin{gathered} x=0 \\ \Rightarrow f(x)=15 \end{gathered}`

(0,15). This is the number of gallons in the tank when we have driven 0 miles.