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

Answer:

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

Step-by-step 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 $5$,

$f(d)=11+2\times3.5=18$

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

$f(d)=11+(6-4)\times3.5=18$

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

$f(d)=11+(d-4)\times3.5$

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

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

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