Graph Analysis: Determining Uniform vs Non-uniform Rate of Change

Question

Given the following graph, determine whether the rate of change is uniform or not

–5–5–5–4–4–4–3–3–3–2–2–2–1–1–1111222333444555666777888999101010111111–3–3–3–2–2–2–1–1–1111222333444555000

Video Solution

Solution Steps

00:00 Is the rate of change of the function uniform?
00:03 We want to check if the value differences in X and Y are constant
00:06 For this, we'll take some points on the graph and observe the rate of change
00:19 Let's calculate the differences between X values
00:23 The differences in X values are equal
00:26 Let's calculate the differences between Y values
00:39 We can see that the differences between Y values are not equal
00:45 Therefore, the rate of change is not uniform
00:50 And this is the solution to the question

Step-by-Step Solution

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.

Answer

Non-uniform

More Questions

Related Subjects

Variation of a Function Rate of Change of a Function Variable Rate of Change Rate of Change of a Function Represented by a Table of Values Constant Rate of Change Rate of change of a function represented graphically Rate of change represented with steps in the graph of the function

Question Types

Variation of a Function: Calculate the rate of change in a graph