Analyzing Rate of Change: Function Table with X-Y Coordinates (1,2) to (4,7)

To solve this problem, we'll follow these steps:

• Step 1: Calculate the rate of change between the first pair of points $(1, 2)$ and $(2, 3)$.
• Step 2: Calculate the rate of change between the second pair of points $(2, 3)$ and $(3, 4)$.
• Step 3: Calculate the rate of change between the third pair of points $(3, 4)$ and $(4, 7)$.
• Step 4: Compare the calculated rates to determine uniformity.

Step 1: Calculate the slope between $(1, 2)$ and $(2, 3)$
$\text{Slope} = \frac{3 - 2}{2 - 1} = 1$

Step 2: Calculate the slope between $(2, 3)$ and $(3, 4)$
$\text{Slope} = \frac{4 - 3}{3 - 2} = 1$

Step 3: Calculate the slope between $(3, 4)$ and $(4, 7)$
$\text{Slope} = \frac{7 - 4}{4 - 3} = 3$

Step 4: Compare the slopes:
The slopes between the first two pairs of points are equal to 1, while the slope between the last pair of points is 3. Since these slopes are not equal, the rate of change is not uniform.

Therefore, the solution to the problem is that the rate of change is non-uniform.