Question

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

Answer 1

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]}