Question

key features of trigonometric functions: mastery test select all the correct answers. which statements are true about the graphed function? the amplitude of the function is 2.5. the amplitude of the function is 4. the period of the function is π. the midline of the function is y = 1.5. the period of the function is 2π. the midline of the function is y = 1.

Explanation:

Step1: Recall amplitude formula

Amplitude $A=\frac{\text{max}-\text{min}}{2}$. From the graph, $\text{max} = 4$ and $\text{min}= - 1$. So $A=\frac{4 - (-1)}{2}=\frac{5}{2}=2.5$.

Step2: Determine the period

The period is the horizontal distance between two consecutive peaks or troughs. From the graph, the distance between two consecutive peaks (e.g., from $x = 0$ to $x=2\pi$) is $2\pi$.

Step3: Find the mid - line

The mid - line is $y=\frac{\text{max}+\text{min}}{2}=\frac{4+( - 1)}{2}=\frac{3}{2}=1.5$.

Answer:

The amplitude of the function is 2.5.
The period of the function is $2\pi$.
The midline of the function is $y = 1.5$.