Question

Use the Table to answer th question
x f(x) g(x)
-2 -7 -1
-1 0 0
0 1 1
1 2 2
2 9 3

questions
Compare the functions f(x) and g(x). At how many points do the functions intersect?
The functions f(x) and g(x) intersects at __ data points

Answer 1

To determine at how many points the functions \( f(x) \) and \( g(x) \) intersect, we need to compare the values of \( f(x) \) and \( g(x) \) for the given \( x \) values.

Here are the provided values from the table:

\[
\begin{array}{|c|c|c|}
\hline
x & f(x) & g(x) \\
\hline
-2 & -7 & -1 \\
-1 & 0 & 0 \\
0 & 1 & 1 \\
1 & 2 & 2 \\
2 & 9 & 3 \\
\hline
\end{array}
\]

Now we will check each \( x \) value to see where \( f(x) = g(x) \):

1. For \( x = -2 \): \( f(-2) = -7 \) and \( g(-2) = -1 \) → not equal
2. For \( x = -1 \): \( f(-1) = 0 \) and \( g(-1) = 0 \) → equal (intersection point)
3. For \( x = 0 \): \( f(0) = 1 \) and \( g(0) = 1 \) → equal (intersection point)
4. For \( x = 1 \): \( f(1) = 2 \) and \( g(1) = 2 \) → equal (intersection point)
5. For \( x = 2 \): \( f(2) = 9 \) and \( g(2) = 3 \) → not equal

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

Thus, the answer is:

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