drag the slider to change the value of h, and observe the effect of h on the graph of the cosine function…

drag the slider to change the value of h, and observe the effect of h on the graph of the cosine function. when h = π, the orange graph shifts units to the. when h = -π, the orange graph shifts units to the. done

drag the slider to change the value of h, and observe the effect of h on the graph of the cosine function. when h = π, the orange graph shifts units to the. when h = -π, the orange graph shifts units to the. done

Answer

Explanation:

Step1: Recall horizontal - shift rule

For the function $y = f(x - h)$, a positive $h$ shifts the graph of $y = f(x)$ to the right by $h$ units and a negative $h$ shifts it to the left by $|h|$ units.

Step2: Analyze $h=\pi$ case

For the cosine function $y=\cos(x - h)$, when $h = \pi$, we have $y=\cos(x-\pi)$. According to the rule, the graph of $y = \cos(x)$ shifts $\pi$ units to the right.

Step3: Analyze $h =-\pi$ case

When $h=-\pi$, we have $y=\cos(x-(-\pi))=\cos(x + \pi)$. According to the rule, the graph of $y=\cos(x)$ shifts $\pi$ units to the left.

Answer:

When $h = \pi$, the orange graph shifts $\pi$ units to the right. When $h=-\pi$, the orange graph shifts $\pi$ units to the left.