Analyzing Rate of Change: Determine Uniformity from X-Y Coordinate Table

Question

Given a table showing points on the graph of a function, determine whether or not the rate of change is uniform.

00:16 Let's check if the rate of change is the same throughout.

00:22 Notice how the change in X values is consistent.

00:29 And the change in Y values stays the same too.

00:33 So, the rate of change is uniform.

00:36 And that's how we solve this problem.

To determine whether the rate of change is uniform for the function given by the table, follow these steps:

Let's calculate the rate of change between these points:

1. Between $(-7, 0)$ and $(-4, 1)$ :
The rate of change is:
$\frac{1 - 0}{-4 - (-7)} = \frac{1}{3}.$

2. Between $(-4, 1)$ and $(-1, 2)$ :
The rate of change is:
$\frac{2 - 1}{-1 - (-4)} = \frac{1}{3}.$

3. Between $(-1, 2)$ and $(2, 3)$ :
The rate of change is:
$\frac{3 - 2}{2 - (-1)} = \frac{1}{3}.$

All calculated rates of change are equal to $\frac{1}{3}$ , indicating the rate of change is uniform between each consecutive pair of points.

Therefore, the rate of change is Uniform.

Uniform