Variable Rate of Change

🏆Practice variation of a function

Variable Rate of Change

The meaning of a variable rate of change of a function can be seen when the variablesX X change in fixed proportions and the Y Y change unevenly. 

A variable rate of change is represented by a line that is not straight, as seen in the following diagram:

B3 - Function with inconsistent rate of change

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

111222333444555666111222333000

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How can the variable rate of change of a function be identified?

For example, if the constant interval of the X X is 2 2 and that of the Y Y is not constant and varies from time to time.
An inconsistent interval could be:
1,3,7,13 1,3,7,13
If the function is not represented with a straight graph, it means that the rate of change is not constant.
Each part of the function will have a different rate of change, a different slope.

Graph of the Variable Rate of Change

Graph of the inconsistent rate of change


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Table of the Variable Rate of Change

Table representation of a function with a non-constant rate of change

Table representation of a function with a non-constant rate of change


Graph of the stepwise non-constant rate of change

image1 Graph of the non-constant rate of change with steps


If you are interested in this article, you might also be interested in the following articles:

Rate of change of a function

Rate of change of a function represented graphically

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

Constant rate of change

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

In the blog of Tutorela you will find a variety of articles with interesting explanations about mathematics


Examples and exercises with solutions of variable rate of change

Exercise #1

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

111222333444555666111222333000

Video Solution

Answer

Uniform

Exercise #2

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

111222333444555666777888999101010111111121212131313141414151515111222333444555666777888000

Video Solution

Answer

Non-uniform

Exercise #3

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

111222333444555666777888999101010111111121212111222333444555666000

Video Solution

Answer

Non-uniform

Exercise #4

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

111222333444555666777888999101010111111121212111222333444555666000

Video Solution

Answer

Uniform

Exercise #5

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

–6–6–6–5–5–5–4–4–4–3–3–3–2–2–2–1–1–1111222333444555666777888–3–3–3–2–2–2–1–1–1111222333444000

Video Solution

Answer

Uniform

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