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Using the table Compare f(x) and g(x). At how many points do the functions intersect?

x f(x) g(x)
-2 -7 -1
-1 0 0
0 1 1
1 2 2
2 9 3


(1 point)
Responses

1
1

3
3

They do not intersect
They do not intersect

2

1 answer

To determine how many points the functions \( f(x) \) and \( g(x) \) intersect, we need to identify the values of \( x \) where \( f(x) = g(x) \).

Looking at the values provided in the table:

  • For \( x = -2 \): \( f(-2) = -7 \) and \( g(-2) = -1 \) (not equal)
  • For \( x = -1 \): \( f(-1) = 0 \) and \( g(-1) = 0 \) (equal)
  • For \( x = 0 \): \( f(0) = 1 \) and \( g(0) = 1 \) (equal)
  • For \( x = 1 \): \( f(1) = 2 \) and \( g(1) = 2 \) (equal)
  • For \( x = 2 \): \( f(2) = 9 \) and \( g(2) = 3 \) (not equal)

From this analysis, we see that \( f(x) \) and \( g(x) \) intersect at the following points:

  • \( x = -1 \)
  • \( x = 0 \)
  • \( x = 1 \)

Thus, the functions intersect at 3 points.

The correct response is: 3