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Graphing Exponential Functions:
Step-by-Step Instructions
(page 2 of 4)

Sections: Introductory concepts, Step-by-step graphing instructions, Worked examples

To graph an exponential, you need to plot a few points, and then connect the dots and draw the graph, using what you know of exponential behavior:

• Graph y = 3x
• Since 3x grows so quickly, I will not be able to find many reasonably-graphable points on the right-hand side of the graph. And 3x will very quickly get very small on the left-hand side of the graph, so I probably won't find many useful plot-points there, either. I will find a few plot-points in the middle, close to the origin, and then draw the graph from there.

Here is my T-chart:

 <= way too small to plot <= maybe too small <= reasonable <= fine <= fine <= getting kind of big <= way too big

While I have seven plot-points in my T-chart, only as many as five are reasonable to plot. So I plot them:

 plotted points

I'd better not try to continue the line as a quadratic:

 incorrect graph

...or as a straight-ish or only vaguely curved line:

 incorrect graph

The exponential, remember, will get (and stay) very close to zero on the left-hand side, so I will draw the graph "skinnying along" the top of the x-axis on the left-hand side:

 drawing the left-hand side

And on the right-hand side, the exponential will get really big, so I'll draw it shooting up through the top of my graph:

 drawing the right-hand side

Then the exponential graphs as:

 solution

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 Cite this article as: Stapel, Elizabeth. "Graphing Exponential Functions: Step-by-Step Instructions."     Purplemath. Available from http://www.purplemath.com/modules/graphexp2.htm.     Accessed [Date] [Month] 2016

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