Question

A jeepney ride cost 11 pesos for the first 4 kilometers and each additional integer kilometers adds 3.50 pesos to the fare, use a piece-wise function to represent the jeepney fare in terms of the distance f(d) in kilometers.

Answer 1

`f(d)=\left\{ \begin{matrix} 11 & \text{for} & 0< d\leq 4 \\-3+3.5d & \text{for}& d > 4 \end`

Explanation:

Cost of first 4 kilometers ride = 11 pesos.

So, for the first 4 km, the fair is constant i.e.

for 1 km the fare is 11 pesos,

for 2 km the fair is also 11 pesos,

similarly, for 3 km of 4 km, the fare is 11 pesos.

Hence, for the distance
`0\geq d\geq 4`, the fair function,

`f(d)=11\cdots(i)`

After 4 km, there is an increment of $ 3.50 for each kilometer.

So, the fare function up to 5 kilometers,

`f(d)=11+3.5=14.5`

So, the fare function up to 6 kilometers, i.e for the distance
`5<d\leq6`,

`f(d)=11+2*3.5=18`

This can be arranged as the fare function up to 6 km,

`f(d)=11+(6-4)*3.5=18`

Similarly, the fare function up to
`d` kilometer
`(n>4)`,

`f(d)=11+(d-4)*3.5`

`\Rightarrrow f(d)=-3+3.5d\cdots(ii)`

Hence, from equations (i) and (ii),

`f(d)=\left\{ \begin{matrix} 11 & \text{for}\; 0< d \leq 4 \\-3+3.5d & \text{for}\; d > 4 \end`