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
(1 point)
Responses

2
2

1
1

3
3

0

Answer 1

To determine the number of intersection points between the functions \( f(x) \) and \( g(x) \) based on the provided table, we analyze the values of \( f(x) \) and \( g(x) \) at each given \( x \):

\[
\begin{array}{|c|c|c|}
\hline
x & f(x) & g(x) \\
\hline
-2 & 0 & 0 \\
-1 & 1.75 & 1 \\
0 & 2 & 2 \\
1 & 2.25 & 3 \\
2 & 4 & 4 \\
\hline
\end{array}
\]

Next, we evaluate where \( f(x) = g(x) \):

- At \( x = -2 \): \( f(-2) = 0 \) and \( g(-2) = 0 \) → **Intersection**
- At \( x = -1 \): \( f(-1) = 1.75 \) and \( g(-1) = 1 \) → **No Intersection**
- At \( x = 0 \): \( f(0) = 2 \) and \( g(0) = 2 \) → **Intersection**
- At \( x = 1 \): \( f(1) = 2.25 \) and \( g(1) = 3 \) → **No Intersection**
- At \( x = 2 \): \( f(2) = 4 \) and \( g(2) = 4 \) → **Intersection**

Counting the intersections:
- Intersection points found: \( x = -2 \), \( x = 0 \), and \( x = 2 \).

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

Final answer: **3**