Question

A 2-column table with 6 rows. The first column is labeled x with entries negative 4, negative 2, 0, 2, 4, 6. The second column is labeled f of x with entries 0, 2, 8, 2, 0, negative 2.
What are all of the x-intercepts of the continuous function in the table?

(0, 8)
(–4, 0)
(–4, 0), (4, 0)
(–4, 0), (0, 8), (4, 0)

Answer 1

The x-intercepts of a function are the points where the function crosses the x-axis, which means the value of \( f(x) \) is zero at those points.

Given the table:

\[
\begin{array}{cc}
x & f(x) \\
\hline
-4 & 0 \\
-2 & 2 \\
0 & 8 \\
2 & 2 \\
4 & 0 \\
6 & -2 \\
\end{array}
\]

We can see that the value of \( f(x) \) is zero at \( x = -4 \) and \( x = 4 \). Therefore, the x-intercepts are at \((-4, 0)\) and \( (4, 0) \).

So, the correct answer is:

\((–4, 0), (4, 0)\)