Question

Use the table to answer the question.

x f(x) g(x)
−2 −7 −1
−1 0 0
0 1 1
1 2 2
2 9 3
Compare the functions f(x) and g(x) . At how many points do the functions intersect?

(1 point)
The functions f(x)
and g(x)
intersect at
data points.

Answer 1

To find the points of intersection between the functions \( f(x) \) and \( g(x) \), we need to identify where the two functions have the same value, that is, \( f(x) = g(x) \).

Let's compare the values from the table:

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

Now we'll examine each pair of \( f(x) \) and \( g(x) \):

- For \( x = -2 \): \( f(-2) = -7 \) and \( g(-2) = -1 \): Not equal.
- For \( x = -1 \): \( f(-1) = 0 \) and \( g(-1) = 0 \): Equal (intersection).
- For \( x = 0 \): \( f(0) = 1 \) and \( g(0) = 1 \): Equal (intersection).
- For \( x = 1 \): \( f(1) = 2 \) and \( g(1) = 2 \): Equal (intersection).
- For \( x = 2 \): \( f(2) = 9 \) and \( g(2) = 3 \): Not equal.

The functions intersect at three points: \( x = -1, 0, \) and \( 1 \).

Thus, the functions \( f(x) \) and \( g(x) \) intersect at **3 data points**.