Rate of Change Steps Practice Problems & Solutions

Master analyzing rate of change using step method on function graphs. Practice problems with detailed solutions for constant and variable rates.

📚Master Rate of Change Analysis Using the Step Method
  • Draw and interpret steps on function graphs to visualize rate of change
  • Identify constant rate of change when step heights remain equal
  • Recognize increasing rate of change from growing step heights
  • Analyze decreasing rate of change through diminishing step heights
  • Compare X-axis intervals with Y-axis changes using visual steps
  • Apply step method to determine if functions have variable rates

Understanding Rate of change represented with steps in the graph of the function

Complete explanation with examples

Rate of change represented by steps in the function graph

We can draw stairs on the graph of the function to see the rate of change.
The base of the step will represent the interval in the X X variables and the height will symbolize the interval in the Y Y .

The step will mark the "jump" from X X in relation to the "jump" in Y Y .
The bases of the steps will always be the same since we always choose fixed intervals in X X .

  • If the heights of the steps are increasing, it means that the rate of change is increasing.
  • If the heights of the steps are decreasing, it means that the rate of change is decreasing.
  • If the heights of the steps do not change, it means that the rate of change is constant.
Rate of change represented by steps in the function graph

Detailed explanation

Practice Rate of change represented with steps in the graph of the function

Test your knowledge with 9 quizzes

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

XY1234-6-303

Examples with solutions for Rate of change represented with steps in the graph of the function

Step-by-step solutions included
Exercise #1

Look at the graph below and determine whether the function's rate of change is constant 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

Step-by-Step Solution

First we need to remember that if the function is not a straight line, its rate of change is not constant.

The rate of change is not uniform since the function is not a straight line.

Answer:

Not constant

Video Solution
Exercise #2

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

111222333444555666777888999101010111111121212131313141414151515111222333444555666777888000

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.

Answer:

Non-uniform

Video Solution
Exercise #3

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

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.

Answer:

Non-uniform

Video Solution
Exercise #4

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

–8–8–8–7–7–7–6–6–6–5–5–5–4–4–4–3–3–3–2–2–2–1–1–1111222333444555666777888–3–3–3–2–2–2–1–1–1111222333444555666000

Step-by-Step Solution

Remember that if the function is a straight line, its rate of change will be constant.

Due to the fact that the graph is a straight line - the rate of change is constant.

Answer:

Uniform

Video Solution
Exercise #5

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

Step-by-Step Solution

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 x there is a proportional and consistent change in y 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 y changes for each unit change in x 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

Answer:

Non-uniform

Video Solution

Frequently Asked Questions

Everything you need to know about Rate of change represented with steps in the graph of the function

How do you use steps to find rate of change on a graph?

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Draw rectangular steps on the function graph where the base represents fixed X intervals and the height shows Y changes. Compare step heights: equal heights mean constant rate, increasing heights show accelerating rate, and decreasing heights indicate slowing rate.

What does it mean when all step heights are the same?

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When all step heights are equal on a function graph, it indicates a constant rate of change. This typically occurs with linear functions where the slope remains the same throughout the entire domain.

Why do step bases stay the same but heights change?

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Step bases remain constant because we choose fixed intervals on the X-axis for consistent comparison. The heights vary because they represent the corresponding Y-value changes, which reveal how the rate of change behaves across different parts of the function.

How can you tell if a rate of change is increasing or decreasing?

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Compare step heights from left to right: 1) Increasing heights = increasing rate of change, 2) Decreasing heights = decreasing rate of change, 3) Constant heights = constant rate of change.

What type of graph paper is best for the step method?

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Use graph paper with clearly marked squares where you know the exact length and height measurements. This allows you to accurately draw steps and make precise comparisons of rate changes across the function.

Can you use the step method on curved functions?

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Yes, the step method works excellently on curved functions to visualize how the rate of change varies. Curved functions typically show variable step heights, making this method particularly useful for understanding non-linear behavior.

What's the difference between constant and variable rate of change using steps?

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Constant rate: All steps have identical heights (straight line). Variable rate: Step heights change as you move along the graph (curved line). The visual comparison makes this difference immediately apparent.

How do you practice analyzing rate of change with steps?

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Start with simple linear functions to see constant step heights, then progress to quadratic and other curved functions. Practice drawing steps with consistent X-intervals and measuring the corresponding Y-changes to build pattern recognition skills.

More Rate of change represented with steps in the graph of the function Questions

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Variation of a Function

Find the Rate of Change: Solving -x+y=0 Linear Equation Find the Rate of Change in the Linear Equation: -5x+y=3 Find the Rate of Change in the Linear Equation 3-y=1/4x Find the Rate of Change in Linear Equation -8y+2x=6 Find the Rate of Change: Solving -1/4y + x = 3

Continue Your Math Journey

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