Analyzing Rate of Change: Function Table with X-Values 1-4 and Y-Values -6 to 3

Q: What exactly does 'uniform rate of change' mean?

A uniform rate of change means the function increases (or decreases) by the same amount for every unit change in x. It's like climbing stairs with equal steps!

Q: Do I need to check all pairs or just some?

You must check all consecutive pairs of points! Even if the first two slopes match, the third could be different. Missing one calculation could give you the wrong answer.

Q: What if I get different slopes for different pairs?

Then the rate of change is non-uniform! This means the function doesn't increase at a constant rate - it could be curved or have varying steepness.

Q: Why is the change in x always 1 in this problem?

The x-values go 1, 2, 3, 4 - so $ \Delta x = 1 $ for each step. This makes calculating easier since slope = $ \frac{\Delta y}{1} = \Delta y $.

Rate of Change with Function Tables

Given a table showing points on the graph of a function, determine whether or not the rate of change is uniform.

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Determine if the rate of change is uniform?

00:06 It appears that the change in X values is always equal

00:12 It appears that the change in Y values is always equal

00:19 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Given a table showing points on the graph of a function, determine whether or not the rate of change is uniform.

Step-by-step solution

To determine if the rate of change is uniform, we need to calculate the slope between each pair of consecutive points and check for consistency.

Let's compute the slopes:

Between $(1, -6)$ and $(2, -3)$ :
$\Delta y = -3 - (-6) = 3$
$\Delta x = 2 - 1 = 1$
Slope $= \frac{3}{1} = 3$
Between $(2, -3)$ and $(3, 0)$ :
$\Delta y = 0 - (-3) = 3$
$\Delta x = 3 - 2 = 1$
Slope $= \frac{3}{1} = 3$
Between $(3, 0)$ and $(4, 3)$ :
$\Delta y = 3 - 0 = 3$
$\Delta x = 4 - 3 = 1$
Slope $= \frac{3}{1} = 3$

Since the slopes are all equal, the rate of change is the same between each pair of consecutive points.

Therefore, the rate of change is uniform.

Final Answer

Uniform

Key Points to Remember

Essential concepts to master this topic

Uniform Rate: All consecutive slopes must be exactly equal
Technique: Calculate $\frac{\Delta y}{\Delta x}$ between each pair: $\frac{3}{1} = 3$
Check: Compare all slopes: 3 = 3 = 3 confirms uniform rate ✓

Common Mistakes

Avoid these frequent errors

Only checking one pair of points
Don't calculate slope for just two points and assume uniformity = missing the whole pattern! You need to check ALL consecutive pairs to confirm consistency. Always calculate every slope between adjacent points to verify uniform rate.

Practice Quiz

Test your knowledge with interactive questions

Look at the graph below and determine whether the function's rate of change is constant or not:

FAQ

Everything you need to know about this question

What exactly does 'uniform rate of change' mean?

A uniform rate of change means the function increases (or decreases) by the same amount for every unit change in x. It's like climbing stairs with equal steps!

Do I need to check all pairs or just some?

You must check all consecutive pairs of points! Even if the first two slopes match, the third could be different. Missing one calculation could give you the wrong answer.

What if I get different slopes for different pairs?

Then the rate of change is non-uniform! This means the function doesn't increase at a constant rate - it could be curved or have varying steepness.

Can the rate be uniform if it's negative?

Absolutely! A uniform rate can be negative (like -2, -2, -2). This just means the function is decreasing at a constant rate instead of increasing.

Why is the change in x always 1 in this problem?

The x-values go 1, 2, 3, 4 - so $\Delta x = 1$ for each step. This makes calculating easier since slope = $\frac{\Delta y}{1} = \Delta y$ .

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Functions questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime