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:
<=
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:
