question 2 (1 point)\ngiven the periodic function below:\ndetermine:\na) the amplitude.\nb) the axis.\nc)…

Explanation:

Step1: Find the amplitude

The amplitude is the distance from the axis of the wave to its maximum or minimum. The maximum value is 5 and the minimum is - 1. The axis is at $y = 2$ (calculated as $\frac{5+( - 1)}{2}$). Amplitude $A=\frac{5-( - 1)}{2}=3$.

Step2: Determine the axis

The axis of a periodic - function is the mid - value between the maximum and minimum values. So, $y=\frac{5+( - 1)}{2}=2$.

Step3: Calculate the period

The period is the horizontal distance between two consecutive identical points on the wave. From the graph, we can see that the wave repeats every $\pi$ units. So the period $T = \pi$.

Step4: Find the y - value at $x = 2\pi$

Since the period is $\pi$, when $x = 2\pi$, it is equivalent to $x = 0$ (because $2\pi$ is a multiple of the period $\pi$). At $x = 0$, $y = 2$.

Answer:

a) 3 b) $y = 2$ c) $\pi$ d) 2