Question

Compare the functions f(x) and g(x) shown in the table. At 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 where the functions \( f(x) \) and \( g(x) \) intersect, we need to find the values of \( x \) for which \( f(x) = g(x) \).

From the table you've provided, we can compare the values of \( f(x) \) and \( g(x) \) at each corresponding \( x \):

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

**Let's analyze the pairs:**

1. **At \( x = -2 \)**: \( f(-2) = 0 \), \( g(-2) = 0 \) → \( f(-2) = g(-2) \) → **Intersection** at \( x = -2 \).

2. **At \( x = -1 \)**: \( f(-1) = 1.75 \), \( g(-1) = 1 \) → No intersection.

3. **At \( x = 0 \)**: \( f(0) = 2 \), \( g(0) = 2.25 \) → No intersection.

4. **At \( x = 1 \)**: \( f(1) = 2.25 \), \( g(1) = 3 \) → No intersection.

5. **At \( x = 2 \)**: \( f(2) = 4 \), \( g(2) = 4 \) → \( f(2) = g(2) \) → **Intersection** at \( x = 2 \).

**Summary of Intersections:**

The functions \( f(x) \) and \( g(x) \) intersect at:
- \( x = -2 \)
- \( x = 2 \)

These are the points where the values of \( f(x) \) and \( g(x) \) are equal.