The base Jeepney fare is PHP 8.00 for the first four kilometers and additional PHP 1.50 per kilometers for the succeeding kilometers. Express the fare for x kilometers as a function of x.
If x>4
f = 8 + 1.5 (x-4) = 1.5 x + 2
IF x</=4
f = 8
To express the fare for x kilometers as a function of x, we can break it down into two parts:
1) The fare for the first 4 kilometers, which is PHP 8.00.
2) The fare for the succeeding kilometers, which is PHP 1.50 per kilometer.
Let's denote the fare for x kilometers as F(x). Now, let's write the function step-by-step:
Step 1: Check if x is less than or equal to 4 kilometers.
- If x is less than or equal to 4, then the fare is PHP 8.00. So, F(x) = 8.00.
Step 2: If x is greater than 4 kilometers, we need to calculate the fare for the succeeding kilometers.
- The number of succeeding kilometers will be x - 4, as the first 4 kilometers have already been accounted for.
- Each succeeding kilometer costs PHP 1.50. So, the fare for the succeeding kilometers is (x - 4) * 1.50.
Step 3: Add the fare for the first 4 kilometers and the fare for the succeeding kilometers.
- F(x) = 8.00 + (x - 4) * 1.50.
Therefore, the fare for x kilometers can be expressed as the function F(x) = 8.00 + (x - 4) * 1.50.
To express the fare for x kilometers as a function of x, we need to consider two scenarios: the first four kilometers and the succeeding kilometers.
For the first four kilometers, the fare is PHP 8.00. Since this part of the fare remains constant regardless of the number of kilometers, we can represent it as a fixed value or a constant term in the function.
After the first four kilometers, the fare increases by PHP 1.50 for each additional kilometer. This implies that the fare for the succeeding kilometers can be represented as the product of the additional kilometers (x - 4) and PHP 1.50.
Therefore, the fare for x kilometers can be expressed as the sum of the constant base fare (PHP 8.00) and the fare for the succeeding kilometers:
F(x) = 8.00 + 1.50(x - 4)
Simplifying the equation, we have:
F(x) = 8.00 + 1.50x - 6.00
F(x) = 1.50x + 2.00
So, the fare for x kilometers is given by the function F(x) = 1.50x + 2.00.