Math Lesson 15.5.5 - How do the Values of the Other Coefficients Affect the Graph?

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Welcome to our Math lesson on How do the Values of the Other Coefficients Affect the Graph?, this is the fifth lesson of our suite of math lessons covering the topic of Exponential Graphs, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.

How do the Values of the Other Coefficients Affect the Graph?

Now, let's see how the other coefficients k and m affect the graph shape of an exponential graph of the form

For this analysis, we will use the help of the corresponding parent graph y = ax.

Let's begin with the coefficient k first. Thus, the greater the coefficient k, the faster the increase in the values of y. This brings a narrower graph compared to the corresponding parent graph. On the other hand, every decrease in the value of the coefficient k results in a wider graph compared to the parent one. For example, the graph of y = 3 · 2x is narrower than y = 2x, and y = 0.4 · 2x is wider than y = 2x · 2x, as shown in the figure below.

The same thing is true for the other coefficient m as well. Thus, when m increases, the graph becomes narrower as the y-values increase faster than before and when m decreases the graph becomes wider, as the y-values increase slower than before. Look at the figure below in which the graphs of three exponential functions, y = 2x, y = 22x and y = 20.5x are shown.

You have reached the end of Math lesson 15.5.5 How do the Values of the Other Coefficients Affect the Graph?. There are 8 lessons in this physics tutorial covering Exponential Graphs, you can access all the lessons from this tutorial below.

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