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

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

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

• Step 1: Calculate the slope between points:
• For $(-2, 3)$ to $(0, 5)$:
$m_1 = \frac{5 - 3}{0 + 2} = \frac{2}{2} = 1$
• For $(0, 5)$ to $(2, 8)$:
$m_2 = \frac{8 - 5}{2 - 0} = \frac{3}{2}$
• For $(2, 8)$ to $(4, 12)$:
$m_3 = \frac{12 - 8}{4 - 2} = \frac{4}{2} = 2$
• 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.