Question

x | y
0 | -2
2 | 4
4 | 10
6 | 16
Which of the following equations correctly describes the function in the table using function notation?

Answer 1

To find the equation that describes the function represented by the given points, we can first analyze the data:

Let's examine the points:
- (0, -2)
- (2, 4)
- (4, 10)
- (6, 16)

Next, we can look for patterns in the \(y\) values based on the \(x\) values.

1. **Calculate the differences in \(y\)**:
- From \(x = 0\) to \(x = 2\): \(4 - (-2) = 6\)
- From \(x = 2\) to \(x = 4\): \(10 - 4 = 6\)
- From \(x = 4\) to \(x = 6\): \(16 - 10 = 6\)

Since the differences in \(y\) are constant (6), this indicates that the relation is linear.

2. **Determine the slope \(m\)**:
The slope (\(m\)) can be calculated as:
\[
m = \frac{\text{change in } y}{\text{change in } x} = \frac{6}{2} = 3
\]

3. **Find the y-intercept \(b\)**:
We can use the slope and one point to find the y-intercept. Using the point (0, -2):
\[
y = mx + b \\
-2 = 3(0) + b \\
b = -2
\]

4. **Write the function**:
The equation that describes the function in the form \(y = mx + b\) is:
\[
y = 3x - 2
\]

In function notation, we can express this as:
\[
f(x) = 3x - 2
\]

Thus, the correct equation that describes the function in the table is:
\[
\boxed{f(x) = 3x - 2}
\]