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

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

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To use this method, you need a graph paper on which we know the length and height of each square. In this way, you can draw "steps" across the entire graph, which will help us compare the height of these steps at different points of the function.

We will demonstrate this with two different graphs drawn on graph paper:

In the first one, there is a straight line in which all the heights of the steps are equal. Consequently, we understand that this is a constant rate of change.

Steps for Signaling a Constant Rate of Change

Steps for signaling a constant rate of change

The second graph represents a function in which the heights of the steps change.

Consequently, we understand that it is a rate of change that is not constant.  

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Question 1

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

Question 2

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

Question 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

Steps for Signaling a Non-Constant Rate of Change

image 2 Steps for signaling a non-constant rate of change

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Rate of change of a function

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Rate of change of a function represented by a table of values

Constant rate of change

Variable rate of change

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Do you know what the answer is?
Question 1

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

111222333444555666777888999101010111111121212131313141414151515111222333444555666777888000

Question 2

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

Question 3

Given the following graph, determine whether function is constant

–9–9–9–8–8–8–7–7–7–6–6–6–5–5–5–4–4–4–3–3–3–2–2–2–1–1–1111222333444555666777888999–4–4–4–3–3–3–2–2–2–1–1–1111222333444555666000

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