Question

standard 15 homework
score: 9/21 answered: 9/20
question 10
determine the amplitude, midline, and period of the function shown above
the amplitude is
the period is
the midline is ( y = )
question help: message instructor post to forum

Explanation:

Step1: Find the amplitude

The amplitude is half the distance between the maximum and minimum values.
The maximum value \( y_{max}=5 \), the minimum value \( y_{min} = 1 \).

$$ \text{Amplitude}=\frac{y_{max}-y_{min}}{2}=\frac{5 - 1}{2}=2 $$

Step2: Find the mid - line

The mid - line is the average of the maximum and minimum values.

$$ y=\frac{y_{max}+y_{min}}{2}=\frac{5 + 1}{2}=3 $$

Step3: Find the period

The period is the horizontal length of one full cycle of the function.
From the graph, one full cycle (from \( x=-4 \) to \( x = 0 \)) has a length of \( 4 \) units.

Answer:

The amplitude is \( 2 \).
The period is \( 4 \).
The midline is \( y = 3 \).