Question

Using the table Compare f(x) and g(x). At how many points do the functions intersect? x f(x) g(x) -2 -7 -1 -1 0 0 0 1 1 1 2 2 2 9 3 (1 point) Responses 3 3 1 1 They do not intersect They do not intersect 2

Answer 1

To determine the number of intersection points between the functions \( f(x) \) and \( g(x) \), we need to identify where their values are equal at the corresponding \( x \) values in the provided table.

Let’s compare the values of \( f(x) \) and \( g(x) \):

\[
\begin{array}{|c|c|c|}
\hline
x & f(x) & g(x) \\
\hline
-2 & -7 & -1 \\
-1 & -1 & 0 \\
0 & 0 & 1 \\
1 & 1 & 2 \\
2 & 2 & 9 \\
3 & 3 & - \\
\hline
\end{array}
\]

Now we point out the values:

1. At \( x = -2 \), \( f(-2) = -7 \) and \( g(-2) = -1 \) (not equal)
2. At \( x = -1 \), \( f(-1) = -1 \) and \( g(-1) = 0 \) (not equal)
3. At \( x = 0 \), \( f(0) = 0 \) and \( g(0) = 1 \) (not equal)
4. At \( x = 1 \), \( f(1) = 1 \) and \( g(1) = 2 \) (not equal)
5. At \( x = 2 \), \( f(2) = 2 \) and \( g(2) = 9 \) (not equal)
6. At \( x = 3 \), \( f(3) = 3 \) (there is no value for \( g(3) \) given)

From this comparison, we conclude that there are no points at which \( f(x) \) and \( g(x) \) are equal based on the values provided.

Thus, the answer is:

**They do not intersect** (0 points).