Question

What set describes the zeroes of the function f(x )= 6πsin(4x) shown in the graph?

Answer 1

Answer:

"$[x|x=\frac{k}{4}\pi]$ for every integer $k$"

Step-by-step explanation:

The function has zeroes at the x-intercepts in the graph.

If you look at the graph from 0 to $\pi$, you will see that the graph cuts the x-axis at 4 points.

They are at half of $\frac{\pi}{2}$, which is $\frac{\pi}{4}$, at $\frac{\pi}{2}$, at half point between $\frac{\pi}{2}$ and $\pi$, which is at $\frac{3\pi}{4}$, and at $\pi$.

They are basically all multiples of $\frac{\pi}{4}$.

Looking at the answer choices, the third choice is correct.

Plugging in k=1, k=2, k=3, and k=4 into the equation, we see that the zeroes are exactly what we saw. Also, the negative side of the function holds true as well.

Third answer choice is right.