Use the table to answer the question.

Question

x f(x) g(x)
−2 −7 −1
−1 0 0
0 1 1
1 2 2
2 9 3
Compare the functions f(x) and g(x) . At how many points do the functions intersect?

(1 point)
The functions f(x) and g(x) intersect at _ data points.

Answer 1

To find the points of intersection between the functions \( f(x) \) and \( g(x) \), we look for values of \( x \) where \( f(x) = g(x) \).

From the table:

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

The functions \( f(x) \) and \( g(x) \) intersect at 3 data points: for \( x = -1 \), \( x = 0 \), and \( x = 1 \).

Thus, the functions \( f(x) \) and \( g(x) \) intersect at 3 data points.