Question

A 2-column table with 6 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1, 2, 3. The second column is labeled f of x with entries negative 10, negative 8, negative 6, negative 4, negative 2, 0.
Which is an x-intercept of the continuous function in the table?

(0, –6)
(3, 0)
(–6, 0)
(0, 3)

Answer 1

An x-intercept of a continuous function is a point where the function crosses the x-axis, which means the output value (f(x)) is zero at that point.

Given the table:
\[
\begin{array}{|c|c|}
\hline
x & f(x) \\
\hline
-2 & -10 \\
-1 & -8 \\
0 & -6 \\
1 & -4 \\
2 & -2 \\
3 & 0 \\
\hline
\end{array}
\]

We can see that when \( x = 3 \), \( f(x) = 0 \). Therefore, the x-intercept is:

\[
(3, 0)
\]

So, the correct choice is:

\( (3, 0) \)