Question

Use the table to answer the question. x y −2 4 0 0 2 −4 4 −8 What is the rate of change of this function from −2 to 2?(1 point) The function’s rate of change is .

Answer 1

To find the rate of change of the function from \( x = -2 \) to \( x = 2 \), we'll use the formula for the rate of change:

\[
\text{Rate of Change} = \frac{y_2 - y_1}{x_2 - x_1}
\]

From the table, we have the following points:
- When \( x = -2 \), \( y = 4 \).
- When \( x = 2 \), \( y = -4 \).

Now substituting into the formula:

- \( y_1 = 4 \) (when \( x = -2 \))
- \( y_2 = -4 \) (when \( x = 2 \))
- \( x_1 = -2 \)
- \( x_2 = 2 \)

Calculating the rate of change:

\[
\text{Rate of Change} = \frac{-4 - 4}{2 - (-2)} = \frac{-8}{2 + 2} = \frac{-8}{4} = -2
\]

Thus, the function’s rate of change from \( -2 \) to \( 2 \) is \(-2\).