We have been given that fuel efficiency for a 2007 passenger car was 31.2 mi/gal and the same model of car, the fuel efficiency increased to 35.6 mi/gal in 2012. Also, the gas tank for this car holds 16 gallons of gas.
We need to write a function and graph a linear function that models the distance that each car can travel for a given amount of gas up to one tankful.
Let represent the functions as [tex]d_{1}(x)[/tex] and [tex]d_{2}(x)[/tex] where [tex]d_{1}[/tex] and [tex]d_{2}[/tex] represent the distances traveled by car in years 2007 and 2012 and x represents the number of gallons. Therefore, we can express the required functions as:
[tex]d_{1}(x)=31.2x \text{ and } d_{2}(x) = 35.6x[/tex]
Domain of both these functions are [0,16] and ranges are [0,499.2] and [0,569.6] respectively for years 2007 and 2012.
The difference function will be:
[tex]f(x)=35.6x-31.2x\\ f(x)=4.2x[/tex]
[tex]f(16)=4.2*16=67.2[/tex]
Domain of this function is [0,16] and range is [0,67.2].
The graphs are shown below.
