Sketch the graph of f(x)=3^x and describe the end behavior of the graph?

1 Answer
Mar 21, 2018

#x rarr oo, y rarr oo# (As #x# approaches infinity, #y# approaches infinity)

Explanation:

Let's start by making a simple table of values

Remember, an exponential function has a default horizontal asymptote of #y=0#, as is visible below

Since the only transformation is a vertical compression of #3#, this will be simple to solve:

#f(-3)=3^(-3):# #y=1/27#
#f(-2)=3^(-2):# #y=1/9#
#f(-1)=3^(-1):# #y=1/3#
#f(0)=3^(0):# #y=1#
#f(1)=3^(1):# #y=3#
#f(2)=3^(2):# #y=9#
#f(3)=3^(3):# #y=27#

Remember that when you have an exponent of a negative value #(b^-a)#, #b# becomes the denominator put over #1#, and is put to the positive power of #a#.

The end behavior could be described that:

#x rarr oo, y rarr oo# (As #x# approaches infinity, #y# approaches infinity)

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