Function Variation Practice Problems with Table Analysis

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 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.

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.

The problem asks us to determine if the rate of change in the graph is uniform or not. To do this, we need to examine the graph closely to see whether it is linear.

If a graph is linear, it means it is a straight line, indicating a constant (uniform) rate of change. The slope of a straight line does not change, meaning that for every unit increase in $x$ there is a proportional and consistent change in $y$.

In contrast, if a graph curves or the line is not straight, the rate of change would not be uniform. This is because a curve indicates that the amount $y$ changes for each unit change in $x$ is not constant.

By analyzing the given graph, we can see that it is a non-linear function with a visible curve. Since the line is not straight (it appears as a curved line in the graph), the rate of change of the function is not constant across its range.

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

Consequently, the correct choice, corresponding to a non-uniform rate of change in the graph, is:

Non-uniform

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.