Question

using the table compare f(x) and g(x) AT how many points do the function intersect
-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 \( g(x) \) intersect, we can compare the values given in the table for each corresponding \( x \) value.

Here’s the provided data:

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

Now, we will 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.

From the comparisons, we can see that the functions intersect at:

- \( x = -1 \)
- \( x = 0 \)
- \( x = 1 \)

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