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

1
1

They do not intersect
They do not intersect

2
2

3
3
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page 12 of 12

Answer 1

To determine the number of points at which the functions \( f(x) \) and \( g(x) \) intersect, we need to compare the values of \( f(x) \) and \( g(x) \) for the same \( x \) values from the table provided.

Here are the values:

- 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)

Now, let's count the points where \( f(x) = g(x) \):
1. At \( x = -1 \)
2. At \( x = 0 \)
3. At \( x = 1 \)

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

The correct answer is **3**.