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

3
3

1
1

They do not intersect
They do not intersect

2

Answer 1

To determine how many points the functions \( f(x) \) and \( g(x) \) intersect, we will look for values of \( x \) where \( f(x) = g(x) \).

From 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 (intersection at \( x = -1 \))
- For \( x = 0 \): \( f(0) = 1 \) and \( g(0) = 1 \) → Equal (intersection at \( x = 0 \))
- For \( x = 1 \): \( f(1) = 2 \) and \( g(1) = 2 \) → Equal (intersection at \( x = 1 \))
- For \( x = 2 \): \( f(2) = 9 \) and \( g(2) = 3 \) → Not equal

Counting the points where \( f(x) = g(x) \), we find that they intersect at \( x = -1 \), \( x = 0 \), and \( x = 1 \).

Thus, the functions intersect at **3 points**.

The correct response is: **3**.