Question

A tricycle ride costs ₱10.00 for the first 2 kilometers, and each additional kilometer adds ₱8.00 to the fare. Use a Piecewise Function to represent the tricycle fare in terms of the distance d in kilometers.​

Answer 1

Answer:

$f(d) = 10d \: \: \: \: when \: \: d \leqslant 2 \\ = 8d \: when \: d > 2$

where d = distance traveled & f(d) = fare

Answer 2

SOLUTION

GIVEN

A tricycle ride costs ₱10.00 for the first 2 kilometers, and each additional kilometer adds ₱8.00 to the fare.

TO DETERMINE

Use a Piecewise Function to represent the tricycle fare in terms of the distance d in kilometers.

EVALUATION

Let f(d) be the total fare for the distance of d kilometers.

Now it is given that the tricycle ride costs ₱10.00 for the first 2 kilometers, and each additional kilometer adds ₱8.00 to the fare.

So for d ≤ 2 we have f(d) = 10

For d > 2 we have f(d) = 10 + 8(d - 2)

Hence the required Piecewise Function

$\sf f(d) = \begin{cases} & \sf{ \: \: \: \: \: \: \: \: \: \: 10 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: when \: d \leqslant 2} \\ \\ & \sf{ 10 + 8(d - 2) \: \: \: \: \: \: when \: d > 2} \end{cases}$