How do you graph #y=3(4)^x# and state the domain and range?

1 Answer
F. Javier B.
May 23, 2018

See explanation below

Explanation:

Exponential function is a useful a easy to graph, to describe and many process in nature follow a function like this.

First, note that #y=3·4^x# is not #12^x#

Second: applying this rule #a^(-n)=1/a^n#, we observe that our function is never negative, So for this reason, the image is #(0,+oo)#. Is never zero because there is no number such that #4^x=0#

The domain is obviously #RR# because #y# exists for every value of #x#

By other hand, if we imagine that x grows, the value #y# grows also and our function is increasing

But if #x# grows negatively, by rule mentioned above #y=3·1/4^x# is every time lower and lower, so the graph of function trends to 0 when x trends to #-oo#

There is no x-intercept and only a point y-intercept which is y=3

With this information we plot our function that has an apparience like this
graph{y=3(4^x) [-6.59, 5.884, -0.756, 5.49]}

Related questions
See all questions in Exponential Growth and Decay
Impact of this question
1829 views around the world
You can reuse this answer
Creative Commons License