Graphing Exponential Functions

[anthonych414]

I can't seem to understand the procedure, can anyone post any links to a useful tutorial? I took it this year and it was the only thing I didn't understand, 3 questions about it came in my maths final and I got an 82 (I got everything else right but I made a small calculation mistake in a question involving trig in space), and since I plan on taking AP calculus next year I want to understand the concept.

 

[gb7nash]

There's a limited amount you can do by hand. The most important part of graphing something like y = a^x (a>1) is to notice that:

1) It's monotone increasing
2) It has a horizontal asymptote at y = 0 as x approaches -inf
3) A y-intercept of y = 1
4) The graph gradually gets steeper the farther right you go.
5) The "steepness" depends on a. Larger a means that graph approaches infinity much faster

As far as wanting more detail than this, pick easy values to calculate. e.g.

y = 2^x

x y
1 2
2 4
3 8
4 16

If a is not an integer, just plug in a few values in your calculator and graph it that way.

edit: fixed bullet 3

 

[anthonych414]

Thank you for the help, I now have a better understanding of the concept and I will solve some exercises to perfect my technique.