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 determine how many points the functions \( f(x) \) and \( g(x) \) intersect, we need to compare their values at each given \( x \) value from the table.

Here are 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, let's compare \( f(x) \) and \( g(x) \):

- At \( x = -2 \): \( f(-2) = -7 \), \( g(-2) = -1 \) → Not an intersection.
- At \( x = -1 \): \( f(-1) = 0 \), \( g(-1) = 0 \) → Intersection.
- At \( x = 0 \): \( f(0) = 1 \), \( g(0) = 1 \) → Intersection.
- At \( x = 1 \): \( f(1) = 2 \), \( g(1) = 2 \) → Intersection.
- At \( x = 2 \): \( f(2) = 9 \), \( g(2) = 3 \) → Not an intersection.

Counting the intersections:
- We have intersections at \( x = -1 \), \( x = 0 \), and \( x = 1 \).

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

Final answer:
The functions \( f(x) \) and \( g(x) \) intersect at **3** data points.