Return to the Purplemath home page


Return to the Lessons Index  | Do the Lessons in Order  |  Get "Purplemath on CD" for offline use  |  Print-friendly page

Graphing Exponential Functions: Examples (page 4 of 4)

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

  • Graph y = ex

    This might feel a bit more difficult to graph, because just about all of my y-values will be decimal approximations. But if I round off to a reasonable number of decimal places (one or two is generally fine for the purposes of graphing), then this graph will be fairly easy. I just need to make sure that I've drawn a nice neat graph with a consistent scale on my axes.

T-chart for y = e^x Graph for y = e^x

If the power in an exponential isn't linear (such as "x"), but is instead quadratic (such as "2x2") or something else, then the graph may look different. Also, if there is more than one exponential term in the function, the graph may look different.The following are a couple of examples, just to show you how they work.

  • Graph y = 32x2


    Because the power is a negative quadratic, the power is always negative (or zero). Then this graph should generally be pretty close to the x-axis.


      Copyright Elizabeth Stapel 2002-2011 All Rights Reserved


     T-chart for y = 3  2^(-x^2)


    There are very few points here that are reasonable to graph. I'll join the points I've got, and make sure that I remember to draw the graph as a curvy line:


     Graph for y = 3  2^(-x^2)

  • Graph the following:
    y = [ e^x - e^(-x) ] / 2

    This is actually a useful function (called the "hyperbolic sine function"), but you probably won't see it again until calculus. In any case, I compute points and plot, as usual:

T-chart for y = [ e^x - e^(-x) ] / 2 Graph for y = [ e^x - e^(-x) ] / 2

Sometimes you will see the more-complicated exponential functions like these. At this stage in your mathematical career, though, you will probably mostly be dealing with the standard exponential form. So make sure that you're comfortable with its general shape and behavior.

To review: below are some different variations on the same basic exponential function, with the associated graph below each equation. Note that, even if the graph is moved left or right, or up or down, or is flipped upside-down, it still displays the same curve. Make sure you are familiar with this shape!

y = 2x y = 2x y = 2x
y = 2^x y = -2^x y = 2^(-x)
y = 2x + 3 y = 2x 3 y = 2x
y = 2^x + 3 y = 2^x - 3 y = -2^(-x)
y = 2x 3 y = 2x + 3 y = 2x+3
y = -2^x - 3 y = -2^x + 3 y = -2^(x + 3)
y = 2x+3 y = 2x3 y = 2x3
y = 2^(x + 3) y = 2^(x - 3) y = -2^(x - 3)

<< Previous  Top  |  1 | 2 | 3 | 4  |  Return to Index

Cite this article as:

Stapel, Elizabeth. "Graphing Exponential Functions: Examples." Purplemath. Available from Accessed


  Linking to this site
  Printing pages
  School licensing

Reviews of
Internet Sites:
   Free Help
   Et Cetera

The "Homework

Study Skills Survey

Tutoring from Purplemath
Find a local math tutor

  Copyright 2002-2012  Elizabeth Stapel   |   About   |   Terms of Use


 Feedback   |   Error?