Analyzing Rate of Change: Function Table with X-Values (3,5,7,9)

To determine whether the rate of change is uniform, we will calculate the rate of change between each pair of consecutive points given.

• Step 1: Calculate the rate of change between consecutive points.

Calculate between $(3, -2)$ and $(5, -1)$:

$\frac{-1 - (-2)}{5 - 3} = \frac{1}{2}$

Calculate between $(5, -1)$ and $(7, 3)$:

$\frac{3 - (-1)}{7 - 5} = \frac{4}{2} = 2$

Calculate between $(7, 3)$ and $(9, 7)$:

$\frac{7 - 3}{9 - 7} = \frac{4}{2} = 2$

• Step 2: Analyze the calculated rates of change.

We observe that the calculated rates of change are $\frac{1}{2}$, $2$, and $2$. Since the first calculated rate of change is different from the others, the rate of change between the points is not consistent.

Therefore, the rate of change is non-uniform.