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

1 Answer
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]}