How to write a piecewise function from a story?

Question

a lyft driver charges $5 for the first 2miles of a ride and then $1.20 for each additional mile after that

Answer 1

Let x = number of miles

    f(x) = cost 

 

                            5, if x ≤ 2

f(x) =

             5 + 1.2(x-2), if x > 2 

 

Simplify to obtain:

 

                            5, if x ≤ 2

f(x) = 

              1.2x + 2.6, if x > 2

 

Answer 2

f(x) = {  5                         for      0 ≤ x ≤ 2

             1.20(x + 1)           for       x > 2     }

 

where:

f(x) is the charge

x is number of miles