Question

match the equation to the piece of the function that it represents.
$y = 10z + 60$ $y = 30z$ $y = 40z - 120$ $y = 20z$
from 0 to 3 hours
from more than 3 hours to 6 hours
from more than 6 hours to 12 hours

Explanation:

Step1: Analyze for 0 - 3 hours

We assume a linear - like situation. If we consider the form \(y = mx + b\), for the first interval from \(0\) to \(3\) hours, a simple linear function with a non - zero \(y\) - intercept might not be correct if there is no initial charge for zero hours of some service. A function like \(y = 30z\) could represent a situation where the rate is \(30\) per hour for the first few hours. So for \(0\leq z\leq3\), \(y = 30z\).

Step2: Analyze for 3 - 6 hours

For the interval from more than \(3\) hours to \(6\) hours, we can use a function that takes into account the previous \(3\) hours. Let's assume that for \(z>3\), we start with a base value from the first \(3\) hours. If we consider \(y = 40z-120\), when \(z = 3\), \(y=40\times3 - 120=0\), and for \(3 < z\leq6\), this function can represent the cost for this time - interval.

Step3: Analyze for 6 - 12 hours

For the interval from more than \(6\) hours to \(12\) hours, we can use a new linear function. A function like \(y = 20z\) can represent the cost for this time - interval.

Answer:

From 0 to 3 hours: \(y = 30z\)
From more than 3 hours to 6 hours: \(y = 40z - 120\)
From more than 6 hours to 12 hours: \(y = 20z\)