Rate of Change of a Function Represented by a Table of Values

First we need to remember that if the function is not a straight line, its rate of change is not constant.

The rate of change is not uniform since the function is not a straight line.

To solve this problem, let's analyze the graph of the line:

• Step 1: Identify two points on the line. For simplicity, let's choose the intercept at $x = 1$ and $y = 3$, and another at $x = 6$ and $y = 0$ (assuming these are easily readable points).
• Step 2: Calculate the slope using the formula $\frac{y_2 - y_1}{x_2 - x_1}$.
• Step 3: Substituting in our chosen points, the slope is $\frac{0 - 3}{6 - 1} = \frac{-3}{5}$.
• Step 4: Since the graph is a straight line and the slope is constant, the rate of change is uniform.

Therefore, the graph shows a constant or uniform rate of change.

The solution to the problem is thus Uniform.

Since the correct answer is shown in the multiple-choice option "Uniform", we conclude it matches the analysis result.

Let's remember that if the function is not a straight line, its rate of change is not uniform.

Since the graph is not a straight line - the rate of change is not uniform.

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.

To determine whether the rate of change in the graph is uniform, we must analyze the graph for consistency in slope across its span:

• Step 1: Observe the graph shape.
• Step 2: Check where the line is straight, showing no change in slope, and where it curves or changes slope, indicating non-uniform change.

Now, let's work through these steps:

Step 1: By visually inspecting the graph, note that it does not form a perfectly straight line but rather curves upwards. This indicates variability in the slopes along the graph.

Step 2: Since the graph curves, indicating that the slope is not the same throughout, we conclude that the rate of change is not constant.

The curvature implies that the rate of change is non-uniform, as it varies at different points along the x-axis. Therefore, the slope is inconsistent, confirming non-uniformity.

Therefore, the graph shows a non-uniform rate of change.