To find the points of intersection between the functions \( f(x) \) and \( g(x) \), we need to compare the values of \( f(x) \) and \( g(x) \) at each corresponding \( x \) value from the table.
Using the given data:
-
At \( x = -2 \):
- \( f(-2) = -7 \)
- \( g(-2) = -1 \)
-
At \( x = -1 \):
- \( f(-1) = 0 \)
- \( g(-1) = 0 \)
-
At \( x = 0 \):
- \( f(0) = 1 \)
- \( g(0) = 1 \)
-
At \( x = 1 \):
- \( f(1) = 2 \)
- \( g(1) = 2 \)
-
At \( x = 2 \):
- \( f(2) = 9 \)
- \( g(2) = 3 \)
Now, we look for values of \( x \) where \( f(x) = g(x) \):
- At \( x = -2 \): \( f(-2) \neq g(-2) \) (−7 ≠ −1)
- At \( x = -1 \): \( f(-1) = g(-1) \) (0 = 0), intersection
- At \( x = 0 \): \( f(0) = g(0) \) (1 = 1), intersection
- At \( x = 1 \): \( f(1) = g(1) \) (2 = 2), intersection
- At \( x = 2 \): \( f(2) \neq g(2) \) (9 ≠ 3)
The functions \( f(x) \) and \( g(x) \) intersect at 3 points: at \( x = -1 \), \( x = 0 \), and \( x = 1 \).
Thus, the answer is:
The functions \( f(x) \) and \( g(x) \) intersect at 3 data points.
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