here are graphs of four trigonometric functions. which function has amplitude 3 and mid - line y = 5? select…

Explanation:

Step1: Recall amplitude and mid - line concepts

Amplitude is the distance from the mid - line to the maximum or minimum value of the function. Mid - line is the horizontal line about which the function oscillates.

Step2: Analyze Option A

The mid - line of Option A is $y = 3$ (average of maximum $y = 6$ and minimum $y = 0$). Amplitude is $\frac{6 - 0}{2}=3$, but mid - line is not $y = 5$.

Step3: Analyze Option B

The mid - line of Option B is $y = 4$ (average of maximum $y = 6$ and minimum $y = 2$). Amplitude is $\frac{6 - 2}{2}=2$, so it's not correct.

Step4: Analyze Option C

The mid - line of Option C is $y = 3$ (average of maximum $y = 6$ and minimum $y = 0$). Amplitude is $\frac{6 - 0}{2}=3$, but mid - line is not $y = 5$.

Step5: Analyze Option D

The mid - line of Option D is $y = 5$ (average of maximum $y = 8$ and minimum $y = 2$). Amplitude is $\frac{8 - 2}{2}=3$.

Answer:

D.