Variation of a Function - Examples, Exercises and Solutions

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.

The problem requires us to determine whether the rate of change in a given graph is uniform.

A uniform rate of change corresponds to a constant slope, which is characteristic of a linear graph. First, we'll examine the graphical representation.

Upon observing the graph, we see that it displays a straight horizontal line. A horizontal line on a graph indicates that for any two points $(x_1, y_1)$ and $(x_2, y_2)$, the difference in $y$-values is zero, i.e., $y_2 - y_1 = 0$. This implies that the slope, given by the formula $\frac{y_2 - y_1}{x_2 - x_1}$, is zero and remains constant as we move along the line.

Because the line is horizontal and does not change its slope throughout, the rate of change is indeed uniform across the entire graph.

Therefore, the rate of change is uniform.

To determine if the rate of change in the given graph is uniform, we need to analyze the graph and check if it is a straight line.

Step 1: Check for linearity - The most direct way to determine if the graph has a uniform rate of change is by inspecting it for linearity, which means the graph forms a straight line.

Step 2: Analyze the path - The given SVG code and description imply a straight diagonal line, suggesting a constant slope.

For a linear function, the slope $m = \frac{y_2 - y_1}{x_2 - x_1}$ is constant throughout. As the graph is described as a straight line, any change in $x$ results in a proportional change in $y$, confirming the slope does not vary.

Consequently, the graph displays a uniform rate of change. Therefore, the solution to this problem is uniform.