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How do I graph exponents?

I am struggling in maths and I have finally found how to graph easy equations and use substitution and eliminations and by graphing. My best is substitution. I am about to learn about graphing exponents. 
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Here's a simple exponential function:
y = 2^x = 2x
Make a table of values for corresponding x and y values:
x | 0 | 1 | 2 | -1   | -2
y | 1 | 2 | 4 | 1/2 | 1/4
Now graph each pair as a point (x,y):
(0,1), (1,2), etc.
Now sketch a smooth curve through your points.
Note that the y values get closer and closer to the x axis as you go to the left, but they never touch it. That means the x axis is a horizontal asymptote.