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 find the points of intersection between the functions \( f(x) \) and \( g(x) \), we need to compare the values of \( f(x) \) and \( g(x) \) at each corresponding \( x \) value from the table.

Using the given data:

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

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

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

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

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

Now, we look for values of \( x \) where \( f(x) = g(x) \):

- At \( x = -2 \): \( f(-2) \neq g(-2) \) (−7 ≠ −1)
- At \( x = -1 \): \( f(-1) = g(-1) \) (0 = 0), intersection
- At \( x = 0 \): \( f(0) = g(0) \) (1 = 1), intersection
- At \( x = 1 \): \( f(1) = g(1) \) (2 = 2), intersection
- At \( x = 2 \): \( f(2) \neq g(2) \) (9 ≠ 3)

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

Thus, the answer is:

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