Analyzing Rate of Change: Determine Uniformity in a Function Table (-1 to 2)

Question

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

00:00 Determine if the rate of change is uniform?

00:07 It appears that the change in X values is always equal

00:12 It appears that the change in Y values is always equal

00:16 Therefore the rate of change is uniform

00:20 And this is the solution to the question

To determine if the rate of change is uniform, we will calculate it between consecutive points and compare them step-by-step:

Step 1: Calculate between $(0, -1)$ and $(4, 0)$ .
$\text{Rate of change} = \frac{0 - (-1)}{4 - 0} = \frac{1}{4}$
Step 2: Calculate between $(4, 0)$ and $(8, 1)$ .
$\text{Rate of change} = \frac{1 - 0}{8 - 4} = \frac{1}{4}$
Step 3: Calculate between $(8, 1)$ and $(12, 2)$ .
$\text{Rate of change} = \frac{2 - 1}{12 - 8} = \frac{1}{4}$
Step 4: Compare the rates from each step.

Since the rate of change is consistently $\frac{1}{4}$ between each pair of points, the rate of change is uniform.

Therefore, the solution to the problem is Uniform.

Uniform