How do you graph #y = 3^x# by plotting points?

1 Answer
Jul 10, 2016

Simply calculate the #y# values for a range of #x# values and connect the dots.

Explanation:

I usually start with integer values, some positive, and some negative. Let's go with:
#x = -3#
#x = -2#
#x = -1#
#x = 0#
#x = 1#
#x = 2#
#x = 3#

The corresponding #y# values will be:
#y = 1/27#
#y = 1/9#
#y = 1/3#
#y = 1#
#y = 9#
#y = 27#

So we can see that the graph is quickly approaching zero in the negative region (really we could have seen this simply by observing that #3^x# is simply an increasingly large number in the denominator for negative #x#). In the positives, it is quickly increasing. The final result should be a graph looking like this:

graph{3^x [-5, 5, -2.5, 2.5]}