Analyzing Rate of Change: Function Table from (-2,3) to (4,12)

Question

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

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

00:06 It appears that the change in X values is always equal

00:14 However, the change in Y values is not equal

00:18 Therefore, the rate of change is not uniform

00:21 And this is the solution to the question

To determine if the rate of change is uniform, follow these steps:

m_1 = \frac{5 - 3}{0 + 2} = \frac{2}{2} = 1

m_2 = \frac{8 - 5}{2 - 0} = \frac{3}{2}

m_3 = \frac{12 - 8}{4 - 2} = \frac{4}{2} = 2

Step 2: Compare these slopes:
Since $m_1 = 1$ , $m_2 = \frac{3}{2}$ , and $m_3 = 2$ are not equal, the rate of change is not constant.

Therefore, the rate of change is non-uniform.

Non-uniform