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.