How to Find Average Rate of Change: 5 Ways to Get the Answer

Jun 15, 2020 04:05 PM

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Tripboba.com - We may be already familiar with the concept of rate of change. A rate of change is a rate that describes how one quantity changes in relation to another quantity. If x is the independent variable and y is the dependent variable, then we’ll have:

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Rates of change can be positive or negative. This corresponds to an increase or decrease in the y -value between the two data points. It’s positive when the value of x increases, the value of y increases, and the graph slants upward.

It’s negative when the value of x increases, the value of y decreases, and the graph slants downward. When a quantity does not change over time, it is called a zero rate of change. 

Consequently, there’s the concept of the "average rate of change" (commonly abbreviated as ARC). The change in the value of a quantity divided by the elapsed time. For a function, this is the change in the y-value divided by the change in the x-value for two distinct points on the graph.

Know how to find average rate of change by following the given tutorials in this article!

How to find the average rate of change

Learn how to find average rate of change by understanding this formula:

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The word "slope" may also be referred to as "gradient", "incline" or "pitch", and be expressed as:

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Do you know that special circumstance exists when working with straight lines (linear functions)? That’s where the "average rate of change" (the slope) is constant. No matter where you check the slope on a straight line, you will definitely get the same answer.

On the other hand, when you’re working with non-linear functions, the "average rate of change" is not constant. But, the process of computing the "average rate of change", is the same as was used with straight lines.

How to find the average rate of change of a function

When you learn how to find average rate of change, you are looking for the rate at which (how fast) the function's y-values (output) are changing as compared to the function's x-values (input). When working with functions (of all types), the "average rate of change" is expressed using function notation.

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Do you know that the formula is just a re-write of the following?

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You also have to note the following fact:

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How to find average rate of change over an interval

After learning the formula on how to find average rate of change, now let’s try to find the solution to this given problem.

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How to find average rate of change on a graph

Learn to solve this given problem.

Based on the function g(x) shown in the graph below, find the average rate of change over the interval 1 < x < 4.

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Solution:

If the interval is 1 < x < 4, then you are examining the points (1,1) and (4,2), as seen on the graph. From the first point, let a = 1, and g (a) = 1. From the second point, let b = 4 and g (b) = 2.

Substitute into the formula:

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The average rate of change is 1 over 3, or just 1/3. The y-values change 1 unit every time the x-values change 3 units, on this interval.

How to find average rate of change from a table

Now let’s try to find the solution for a problem which involves the use of a table. The following is an example for you.

Based on the function f(x) shown in the table below, find the average rate of change over the interval 1 < x < 3.

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Solution:

If the interval is 1 < x < 3, then you are examining the points (1,4) and (3,16). From the first point, let a = 1, and f (a) = 4. From the second point, let b = 3 and f (b) = 16.

Substitute into the following formula:

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The average rate of change is 6 over 1, or just 6.

The y-values change 6 units every time the x-values change 1 unit, on this interval.

That’s all about the steps to find the average rate of change. Hopefully, this post will help you to solve your math problem. Don’t forget to get more practice!

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