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
= 3^{x}

Since 3^{x}
grows so quickly, I will not be able to find many reasonably-graphable
points on the right-hand side of the graph. And 3^{x}
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:

...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: