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

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

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 $(5, -1)$:

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

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

• 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.