Question

based on the graph above, determine the amplitude, midline, and period of the function
amplitude:
period:
midline: y =
question help: worked example 1

Explanation:

Step1: Find the amplitude

The amplitude is the distance from the midline to the maximum (or minimum) value. The maximum value is \(y = 4\) and the minimum value is \(y=0\). The mid - line \(y=\frac{4 + 0}{2}=2\). Amplitude \(A=\frac{4-0}{2}=2\)

Step2: Find the period

The period is the length of one full cycle of the function. Looking at the graph, from \(x=-2\) to \(x = 0\) is one - half of a cycle. If half - cycle length is \(2\) (since \(0-(-2)=2\)), then the full - cycle length (period \(T\)) is \(2\).

Step3: Find the mid - line

The mid - line is the horizontal line that the graph oscillates around. We can also calculate it as \(y=\frac{\text{Max}+\text{Min}}{2}\). Since \(\text{Max}=4\) and \(\text{Min}=0\), \(y = 2\)

Answer:

Amplitude: \(2\)
Period: \(2\)
Midline: \(y = 2\)