To determine how many points the functions \( f(x) \) and \( g(x) \) intersect, we need to compare their values at the given \( x \) points in the table.
Let's list the points from the table:
-
For \( x = -2 \):
- \( f(-2) = -7 \)
- \( g(-2) = -1 \)
-
For \( x = -1 \):
- \( f(-1) = 0 \)
- \( g(-1) = 0 \)
-
For \( x = 0 \):
- \( f(0) = 1 \)
- \( g(0) = 1 \)
-
For \( x = 1 \):
- \( f(1) = 2 \)
- \( g(1) = 2 \)
-
For \( x = 2 \):
- \( f(2) = 9 \)
- \( g(2) = 3 \)
Now, let's identify the points of intersection:
- At \( x = -2 \): \( f(-2) \neq g(-2) \)
- At \( x = -1 \): \( f(-1) = g(-1) \)
- At \( x = 0 \): \( f(0) = g(0) \)
- At \( x = 1 \): \( f(1) = g(1) \)
- At \( x = 2 \): \( f(2) \neq g(2) \)
From this, we see that the functions \( f(x) \) and \( g(x) \) intersect at the following points:
- \( x = -1 \)
- \( x = 0 \)
- \( x = 1 \)
Thus, the functions intersect at 3 points.
Conclusion: The functions \( f(x) \) and \( g(x) \) intersect at 3 data points.