Question

Compare the functions f(x) and g(x) shown in the table. At how many points do the functions intersect?
x | f (x) | g (x)
-2 | 0 | 0
-1 | 1.75 | 1
0 | 2 | 2
1 | 2.25 | 3
2 | 4 | 4
A. 2
B. 3
C. 1
D. 0

Answer 1

To find the number of points where the functions \( f(x) \) and \( g(x) \) intersect, we need to look for points where their values are equal, meaning \( f(x) = g(x) \).

By examining the values in the table:

- At \( x = -2 \):
- \( f(-2) = 0 \)
- \( g(-2) = 0 \)
- \( f(-2) = g(-2) \)

- At \( x = -1 \):
- \( f(-1) = 1.75 \)
- \( g(-1) = 1 \)
- \( f(-1) \neq g(-1) \)

- At \( x = 0 \):
- \( f(0) = 2 \)
- \( g(0) = 2 \)
- \( f(0) = g(0) \)

- At \( x = 1 \):
- \( f(1) = 2.25 \)
- \( g(1) = 3 \)
- \( f(1) \neq g(1) \)

- At \( x = 2 \):
- \( f(2) = 4 \)
- \( g(2) = 4 \)
- \( f(2) = g(2) \)

Now let's summarize the points where \( f(x) = g(x) \):
- At \( x = -2 \)
- At \( x = 0 \)
- At \( x = 2 \)

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

The answer is **B. 3**.