Question

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

2

They do not intersect

1


3

Answer 1

To determine the number of points at which the functions \( f(x) \) and \( g(x) \) intersect, we need to find the values of \( x \) for which \( f(x) = g(x) \).

From the table:

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

The functions \( f(x) \) and \( g(x) \) intersect at \( x = -1 \), \( x = 0 \), and \( x = 1 \).

Thus, there are **3 points** of intersection.

So the correct response is:

**3**