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

Analyze Rate of Change: Determining Uniformity in a Semicircular Graph

Q: What exactly is rate of change?

Rate of change measures how much the y-value changes compared to the x-value change. Think of it as slope - how steep the graph is at any point.

Q: Why do curved graphs have non-uniform rate of change?

On a curved graph, the steepness changes as you move along the curve! A semicircle starts steep, becomes less steep at the top, then gets steep again. Changing steepness = non-uniform rate.

Q: How can I tell if a rate is uniform just by looking?

Look at the shape: Straight line = uniform rateAny curve (semicircle, parabola, etc.) = non-uniform rate

Q: What if the graph looks almost straight?

If there's any curvature at all, the rate is non-uniform! Even slight curves mean the slope is changing, which makes the rate of change non-uniform.

Q: Can I calculate the actual rate of change values?

Yes! For any two points, use $ \frac{\text{change in y}}{\text{change in x}} $. On curved graphs, you'll get different values for different intervals, proving it's non-uniform.

Rate of Change with Curved Functions

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

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Understand the problem

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

Step-by-step solution

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.

Final Answer

Non-uniform

Key Points to Remember

Essential concepts to master this topic

Rule: Only straight lines have uniform rate of change
Technique: Check if graph is linear: semicircle = curved = non-uniform
Check: Compare slopes at different points: varying slopes = non-uniform ✓

Common Mistakes

Avoid these frequent errors

Assuming all functions have uniform rate of change
Don't assume every graph has constant rate of change = wrong analysis! Only straight lines have uniform rates. Always examine the shape: curved graphs like circles, parabolas, or semicircles have non-uniform rates of change.

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 compared to the x-value change. Think of it as slope - how steep the graph is at any point.

Why do curved graphs have non-uniform rate of change?

On a curved graph, the steepness changes as you move along the curve! A semicircle starts steep, becomes less steep at the top, then gets steep again. Changing steepness = non-uniform rate.

How can I tell if a rate is uniform just by looking?

Look at the shape:

Straight line = uniform rate
Any curve (semicircle, parabola, etc.) = non-uniform rate

What if the graph looks almost straight?

If there's any curvature at all, the rate is non-uniform! Even slight curves mean the slope is changing, which makes the rate of change non-uniform.

Can I calculate the actual rate of change values?

Yes! For any two points, use $\frac{\text{change in y}}{\text{change in x}}$ . On curved graphs, you'll get different values for different intervals, proving it's non-uniform.

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