Question

"Sarah is renting a car for her weekend trip to the mountains. The total cost of the rental, y, as it relates to the number of miles driven, x, is shown in the graph below.

Fill in the blanks so that the functions below, written to represent this situation, are correct. If necessary, the answer in terms of a decimal, rounded to the nearest hundredth.
f(x)= ______x+________"

Answer 1

`f(x)=(1)/(4)x+25`

Explanation:

Clearly from the graph we could see that it passes through two points (0,25) and (20,30) and also as the graph is linear so with the help of these two points we can find the relation between f(x) and x.

We know that the equation of a line passing through two points (a,b) and (c,d) is given by:

`y-b=(d-b)/(c-a)* (x-a)`

Here we have:

y=f(x) , (a,b)=(0,25) and (c,d)=(20,30).

Hence the equation of this graph is given as:

`f(x)-25=(30-25)/(20-0)* (x-0)\\\\f(x)-25=(5)/(20)* x\\\\f(x)-25=(1)/(4)* x\\\\f(x)=(1)/(4)x+25`

Hence,

`f(x)=(1)/(4)x+25`

Answer 2

So here is the answer to the given question above. Analyzing the given figure, we can see that at 0 miles, the cost is 25. Between 0 and 40 miles, the cost rises by 10. Therefore, the function that would represent this situation would be this: f(x) = (10/40)x+25
f(x) = 1/4 *x+ 25
f(x) = 0.25x + 25
Hope this is the answer that you area looking for.