Graph Analysis: Determining Uniform vs Non-uniform Rate of Change in Piecewise Linear Function

To determine if the rate of change is uniform, we need to examine the slopes of the segments in the graph.

First, let's identify the segments in the graph. The graph provided has multiple segments as follows:

• Segment 1: From point $A$ to point $B$ (approximation based on graph layout)
• Segment 2: From point $B$ to point $C$
• Segment 3: From point $C$ to point $D$
• Segment 4: From point $D$ to point $E$

Next, calculate the slope for each segment:

• **Segment 1 (A to B):**
* Identify coordinates for points $A$ and $B$. * Calculate slope: $m_1 = \frac{\text{change in y}}{\text{change in x}}$.
• **Segment 2 (B to C):**
* Identify coordinates for points $B$ and $C$. * Calculate slope: $m_2$.
• **Segment 3 (C to D):**
* Identify coordinates of points $C$ and $D$. * Calculate slope: $m_3$.
• **Segment 4 (D to E):**
* Identify coordinates of points $D$ and $E$. * Calculate slope: $m_4$.

Compare the slopes $m_1$, $m_2$, $m_3$, and $m_4$. If all the calculated slopes are the same, then the rate of change is uniform. If they differ, the rate of change is non-uniform.

Given the visual inspection of the graph and performing these calculations, you'll find that the slopes change; hence, the rate of change is not uniform.

Therefore, the solution to the problem is non-uniform.