Question

using the table compare f(x) and g(x) AT how many points do the function intercept
-2,-7,-1
-1,0,0
0,1,1
1,2,2
2,9,3

Answer 1

To determine how many points the functions \( f(x) \) and \( g(x) \) intercept, we need to identify where the values of \( f(x) \) equal the values of \( g(x) \) for the given \( x \) values.

Here’s the data you've given in the table format:

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

Now, let’s analyze each row:

1. **For \( x = -2 \)**: \( f(-2) = -7 \) and \( g(-2) = -1 \) → Not an interception
2. **For \( x = -1 \)**: \( f(-1) = 0 \) and \( g(-1) = 0 \) → Interception
3. **For \( x = 0 \)**: \( f(0) = 1 \) and \( g(0) = 1 \) → Interception
4. **For \( x = 1 \)**: \( f(1) = 2 \) and \( g(1) = 2 \) → Interception
5. **For \( x = 2 \)**: \( f(2) = 9 \) and \( g(2) = 3 \) → Not an interception

Now we can summarize the intercepts:

- Intercept points:
- At \( x = -1 \): Both functions equal \( 0 \)
- At \( x = 0 \): Both functions equal \( 1 \)
- At \( x = 1 \): Both functions equal \( 2 \)

Thus, the functions \( f(x) \) and \( g(x) \) intercept at **3 points**: \( x = -1 \), \( x = 0 \), and \( x = 1 \).