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

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 ${a}^{- n} = \frac{1}{a} ^ n$, we observe that our function is never negative, So for this reason, the image is $\left(0 , + \infty\right)$. Is never zero because there is no number such that ${4}^{x} = 0$

The domain is obviously $\mathbb{R}$ 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 $- \infty$

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]}