Question

question 3
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 midline

The midline is the horizontal line that runs exactly between the maximum and minimum values of the function.
The maximum value \(y_{max}=-2\) and the minimum value \(y_{min}=-7\).
The formula for the midline \(y = \frac{y_{max}+y_{min}}{2}\)

$$y=\frac{-2+( - 7)}{2}=\frac{-9}{2}=-4.5$$

Step2: Calculate the amplitude

The amplitude is the distance from the midline to the maximum (or minimum) value of the function.
Using the formula \(A=\vert y_{max}-y_{midline}\vert\) (or \(A=\vert y_{min}-y_{midline}\vert\))

$$A=\vert-2-( - 4.5)\vert=\vert-2 + 4.5\vert = 2.5$$

Step3: Determine the period

The period is the horizontal length of one complete cycle of the function.
From the graph, we can see that one complete cycle (from peak - to - peak or trough - to - trough) occurs over a horizontal distance of \(2\) units.

Answer:

Amplitude: \(2.5\)
Period: \(2\)
Midline: \(y=-4.5\)