Question

Kirsten is driving to a city that is 275 miles away. When Kirsten left home, she had 10 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 the intercepts of that function? What do they represent? Drag and drop the correct numbers or phrases into the boxes to complete the answers.

Answer 1

(a). Assuming consumption is only dependent upon miles driven, the function is defined as :

Amount of gas left after driving x miles :

`f(x)=10-(x)/(25)`

(b). The y-intercept is obviously 10. This represents the initial gas in the tank, 10 gallons.

(c). The x-intercept is the solution to

`0=10-(x)/(25)\\\\10=(x)/(25)\\\\\implies x=250`

The x-intercept is 250. It represents the "distance taken by car to empty the tank".