Question

Identify the amplitude and midline

Answer 1

Amplitude = 4

Midline: y = -3

Explanation:

The provided graph shows a sinusoidal function.

Amplitude

The amplitude of a sinusoidal function is one-half of the positive difference between the maximum and minimum values of the function.

The maximum value of the graphed function is 1 and the minimum value is -7, so:

`\begin{aligned}\sf Amplitude&=\sf (1)/(2)|1-(-7)|\\\\&=\sf (1)/(2)|8|\\\\&=\sf (1)/(2) \cdot 8\\\\&=\sf 4\end{aligned}`

Therefore, the amplitude of the graphed function is 4.

Midline

The midline is the horizontal line located at a y-value that is midway between the maximum and minimum y-values of the function. Since the maximum value of the graphed function is 1 and the minimum value is -7, then:

`\begin{aligned}\textsf{Midline:\quad $y$}&=\sf (1+(-7))/(2)\\\\y&=\sf (-6)/(2)\\\\y&=\sf -3\end{aligned}`

Therefore, the midline of the graphed function is y = -3.