Question

Use the table to answer the 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 determine how many points the functions \( f(x) \) and \( g(x) \) intersect, we need to compare their values at the given \( x \) points in the table.

Let's list the points from the table:

- For \( x = -2 \):
- \( f(-2) = -7 \)
- \( g(-2) = -1 \)

- For \( x = -1 \):
- \( f(-1) = 0 \)
- \( g(-1) = 0 \)

- For \( x = 0 \):
- \( f(0) = 1 \)
- \( g(0) = 1 \)

- For \( x = 1 \):
- \( f(1) = 2 \)
- \( g(1) = 2 \)

- For \( x = 2 \):
- \( f(2) = 9 \)
- \( g(2) = 3 \)

Now, let's identify the points of intersection:
- At \( x = -2 \): \( f(-2) \neq g(-2) \)
- At \( x = -1 \): \( f(-1) = g(-1) \)
- At \( x = 0 \): \( f(0) = g(0) \)
- At \( x = 1 \): \( f(1) = g(1) \)
- At \( x = 2 \): \( f(2) \neq g(2) \)

From this, we see that the functions \( f(x) \) and \( g(x) \) intersect at the following points:
- \( x = -1 \)
- \( x = 0 \)
- \( x = 1 \)

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

**Conclusion:** The functions \( f(x) \) and \( g(x) \) intersect at **3 data points**.