Question

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

Answer 1

To determine the number of intersection points between the functions \( f(x) \) and \( g(x) \), we can analyze the values given in the table:

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

Next, we compare the values of \( f(x) \) and \( g(x) \):

- At \( x = -2 \): \( f(-2) = 0 \) and \( g(-2) = 0 \). (intersection)
- At \( x = -1 \): \( f(-1) = 1.75 \) and \( g(-1) = 1 \). (not an intersection, as \( f(-1) > g(-1) \))
- At \( x = 0 \): \( f(0) = 2 \) and \( g(0) = 2 \). (intersection)
- At \( x = 1 \): \( f(1) = 2.25 \) and \( g(1) = 3 \). (not an intersection, as \( f(1) < g(1) \))
- At \( x = 2 \): \( f(2) = 4 \) and \( g(2) = 4 \). (intersection)

In summary, the functions intersect at the following points:
1. At \( x = -2 \)
2. At \( x = 0 \)
3. At \( x = 2 \)

Thus, the functions \( f(x) \) and \( g(x) \) intersect at **3 points**.