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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:

      

    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
    plotted points

      

      

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

     

      Copyright Elizabeth Stapel 2002-2011 All Rights Reserved

      

    incorrect graph
    WRONG!  An exponential is NOT a quadratic!

      

      

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

      

    incorrect graph
    WRONG! Exponentials bend and stay above the x-axis!

      

      

    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
    Just draw this part along the top of the x-axis.

      

      

    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
    Connect the dots.

      

      

    Then the exponential graphs as:

      

    solution
    Graph of y = 3^x

      

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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
 

 



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