Which of the functions is represented by the table?

Steps to Solve

1. Identify the Pattern in the Table

We need to find a relationship between the values of $x$ and $y$ from the table. Let’s examine the pairs:

• When $x = -1$, $y = -8$
• When $x = 1$, $y = 0$
• When $x = 3$, $y = 8$
• When $x = 5$, $y = 16$

2. Calculate the Change in $y$ Relative to $x$

Next, we find the differences in $y$ for changes in $x$:

• From $x = -1$ to $x = 1$: $$ \text{Change} = 0 - (-8) = 8 $$
• From $x = 1$ to $x = 3$: $$ \text{Change} = 8 - 0 = 8 $$
• From $x = 3$ to $x = 5$: $$ \text{Change} = 16 - 8 = 8 $$

Each time, as $x$ increases by 2, $y$ increases by 8.

3. Determine the Slope

From the above, we can determine the slope ($m$): $$ m = \frac{\Delta y}{\Delta x} = \frac{8}{2} = 4 $$

4. Formulate the Linear Equation

Using the point-slope form of the equation, we can apply the slope we found with one of the points. Taking the point $(1, 0)$: $$ y - 0 = 4(x - 1) $$

5. Convert to Slope-Intercept Form

Rearranging gives: $$ y = 4x - 4 $$

6. Look for Equivalent Functions

Now we can look through the provided functions:

• The equation $y = 4x - 4$ is one of the options.