The table in the image you uploaded appears to describe a tangent function, which is periodic. The values of $f(x)$ include zeros at specific angles, and the function has undefined values (where the tangent function has vertical asymptotes) at certain points.

To determine the period of a tangent function, we know that the period of the basic tangent function, $\tan(x)$, is $\pi$. This means that the values of the function repeat every $\pi$ radians.

Looking at the table:

• The function has zeros at multiples of $\frac{\pi}{4}$ (e.g., $-\frac{\pi}{4}$, $\frac{\pi}{4}$, etc.).
• The undefined values occur at multiples of $\frac{\pi}{2}$, which are the vertical asymptotes of the tangent function.

Since the tangent function repeats every $\pi$, the period of this function is $\pi$, which is one of the options listed.

Answer:

The period of the function is $\pi$.

Let me know if you need further clarification!

Here are some related questions you might find useful:

1. What is the general form of a tangent function?
2. How can you determine the period of any trigonometric function?
3. Why does the tangent function have vertical asymptotes?
4. How does the behavior of tangent functions compare to sine and cosine?
5. What are some transformations that can affect the period of the tangent function?

Tip: To find the period of a tangent function, you can use the formula $\frac{2\pi}{|b|}$, where $b$ is the coefficient of $x$ in the function $f(x) = \tan(bx)$.