please help

Question

you have a car with a fuel efficiency of 30 miles per gallon. Define the function f that has "Number of miles driven" as its independent variable and "Number of gallons used" as its dependent variable. If you drive for 120 miles, you need f(120)=_______gallons of gas in your tank.

Answer 1

The independent variable may change for any reason.  The dependent variable is "locked" once the independent variable has a value.

 

The best clue comes from the sentence,"If you drive for 120 miles, you need f(120)=_______gallons of gas in your tank."

This is y=f(120), where x=120 is the value of the independent variable x and y, or f(x), is the value of the dependent variable.

 

Now, the units are of primary importance.

     f(x) gallons  =  (x miles) / ( (30 miles)/(1 gallon) )      [to divide by a fraction, invert and multiply]

                                             [miles cancel out and you are left with gallons.]

 

The function is:

      f(x) = x/30

 

If you drive for 120 miles, you need f(120) gallons = 4 gallons of gas in your tank."

Answer 2

Hi Jessy,

 

x = number of miles

f(x) = number of gallons

 

f(x) = x/30

 

f(120) = 120/30 = 4  You would need 4 gallons to travel 120 miles with fuel efficiency of 30 mpg.