A proposed train fee would charge 20.00 for the first 5km of travel and 0.75 for each addtional kilometer over the proposed fare

Question

A proposed train fee would charge 20.00 for the first 5km of travel and 0.75 for each addtional kilometer over the proposed fare

Q. Find the fare function f(x) where x represents the number of kilometers traveled

A. f(x) = 16.25+0.75x

why is the answer like that when the number is 20.00? So confusing

Answer 1

I agree with you, but here it is:

20 + 0.75x if x >=5

BUT if x<5, then it is $4 per kilometer as 20/5 = 4

So now the function can be written as

20 + 0.75x if x>=5

4x otherwise

Now the piecewise function can be eliminated if

x is replaced with x-5

20 + 0.75(x-5) =

20 + 0.75x - 3.75

16.25 + 0.75x

Like I said, it do not agree either

nor do I like it.

Moreover, there is somewhat unclear.

If they go only 2 km or 3 km or even 4 km,

is the price still $20 ?

or is it broken down as $4 per km ?

Answer 2

Actually it is totally incorrect. This is a piece-wise function (look that up in your text book!).

f(x) = 20, if 0 < x <= 5

f(x) = 20 + 0.75x, if x > 5