Question

Which of the following equations correctly describes the function in the table using function notation?

x y
0 -2
2 4
4 10
6 16


(1 point)
Responses

f(x)=2x
f of x is equal to 2 x

f(x)=3x−2
f of x is equal to 3 x minus 2

f(x)=x−2
f of x is equal to x minus 2

f(x)=2x+4

Answer 1

To determine which equation correctly describes the function in the table, let's analyze the data points:

- For \( x = 0 \), \( y = -2 \)
- For \( x = 2 \), \( y = 4 \)
- For \( x = 4 \), \( y = 10 \)
- For \( x = 6 \), \( y = 16 \)

We can attempt to derive a linear function that fits these points.

Let's first calculate the differences in \( y \) as \( x \) increases:

- From \( x = 0 \) to \( x = 2 \): \( 4 - (-2) = 6 \)
- From \( x = 2 \) to \( x = 4 \): \( 10 - 4 = 6 \)
- From \( x = 4 \) to \( x = 6 \): \( 16 - 10 = 6 \)

The differences in \( y \) are consistent, indicating the function is linear. The slope \( m \) can be determined as follows:
\[ m = \frac{\Delta y}{\Delta x} = \frac{6}{2} = 3 \]

Using the slope and one of the points, we can use point-slope form to find the equation of the line. Using the point \( (0, -2) \):

The slope-intercept form is:
\[ y = mx + b \]

Substituting \( m = 3 \):
\[ y = 3x + b \]

To find \( b \), we can use the point \( (0, -2) \):
\[ -2 = 3(0) + b \]
\[ b = -2 \]

Thus, the equation is:
\[ y = 3x - 2 \]

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

So, the correct answer is:
- **f(x) = 3x - 2** (f of x is equal to 3 x minus 2)