Question

What is the rate of change of the function represented by the table?

x y
1 -8.5
2 -6
3 -3.5
4 -1


(1 point)
Responses

1
1

2.5
2.5

-1
-1

-2.5
-2.5

Answer 1

To find the rate of change of the function represented by the table, we can calculate the change in \( y \) divided by the change in \( x \) (also known as the slope of the line connecting the points).

We'll calculate the change in \( y \) and the change in \( x \) between any two points. Let's use the points \( (1, -8.5) \) and \( (4, -1) \):

1. Calculate \( \Delta y \):
\[
\Delta y = y_2 - y_1 = -1 - (-8.5) = -1 + 8.5 = 7.5
\]

2. Calculate \( \Delta x \):
\[
\Delta x = x_2 - x_1 = 4 - 1 = 3
\]

3. Now, calculate the rate of change (slope):
\[
\text{Rate of change} = \frac{\Delta y}{\Delta x} = \frac{7.5}{3} = 2.5
\]

The rate of change of the function is \( 2.5 \). Therefore, the answer is:

**2.5**