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

The graph does not represents a function

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

Q: What exactly is rate of change?

Rate of change measures how much the y-value changes for each unit change in x-value. It's the slope of the line at any point on the graph.

Q: How can I tell if a graph is curved or straight?

Look carefully at the graph! A straight line maintains the same direction throughout, while a curved line changes direction - it might start steep and become less steep, or vice versa.

Q: Can a graph have both uniform and non-uniform sections?

Yes! Some graphs have straight sections (uniform rate) and curved sections (non-uniform rate). The overall classification depends on the section you're analyzing.

Q: What if the curve is very slight - is it still non-uniform?

Even a slight curve means the rate of change is non-uniform! The slope is changing, even if it's gradual. Only perfectly straight lines have uniform rates.

Q: Does steepness matter for determining uniform vs non-uniform?

Steepness doesn't matter - only whether the line is straight or curved! A very steep straight line still has uniform rate, while a gentle curve has non-uniform rate.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

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 written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

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

2

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.

3

Final Answer

Non-uniform

Key Points to Remember

Essential concepts to master this topic

Uniform Rate: Straight lines have constant slope throughout
Non-uniform Rate: Curved graphs show changing slope at different points
Visual Check: If the graph curves upward or downward, rate is non-uniform ✓

Common Mistakes

Avoid these frequent errors

Assuming any smooth graph has uniform rate
Don't think that because a graph looks smooth it has uniform rate of change = wrong classification! Smoothness just means continuous, not constant slope. Always check if the graph is perfectly straight or if it curves at any point.

Practice Quiz

Test your knowledge with interactive questions

Given the following graph, determine whether function is constant

FAQ

Everything you need to know about this question

What exactly is rate of change?

+

Rate of change measures how much the y-value changes for each unit change in x-value. It's the slope of the line at any point on the graph.

How can I tell if a graph is curved or straight?

+

Look carefully at the graph! A straight line maintains the same direction throughout, while a curved line changes direction - it might start steep and become less steep, or vice versa.

Can a graph have both uniform and non-uniform sections?

+

Yes! Some graphs have straight sections (uniform rate) and curved sections (non-uniform rate). The overall classification depends on the section you're analyzing.

What if the curve is very slight - is it still non-uniform?

+

Even a slight curve means the rate of change is non-uniform! The slope is changing, even if it's gradual. Only perfectly straight lines have uniform rates.

Does steepness matter for determining uniform vs non-uniform?

+

Steepness doesn't matter - only whether the line is straight or curved! A very steep straight line still has uniform rate, while a gentle curve has non-uniform rate.

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

Rate of Change with Curved Graphs

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