# How do you graph f(x) = 3^(x+1)?

Aug 1, 2015

You have an Exponential Function.

#### Explanation:

This is an Exponential Function which domain will be all the real $x$ while the range will be all the $y > 0$.
Basically the graph of your function will occupy only the first and second quadrant.
When $x$ becomes very large positively your function also becomes large, it tends to INFINITY; for example, if you have $x = 100$ then $y = {3}^{100 + 1} = 5 \times {10}^{47}$!!!!.
On the other hand when $x$ becomes very large negatively your function becomes very small, it tends to ZERO; for example, if you have $x = - 100$ then $y = {3}^{- 100 + 1} = 6 \times {10}^{-} 48$!!!!.

In plotting your function we can focus our attention around the origin choosing values of $x$ not too big or small to allow us to actually "see", on the graph, the points we have.
Let us try with:
$x = - 3$ then $y = {3}^{- 3 + 1} = {3}^{- 2} = 0.11$;
$x = - 2$ then $y = {3}^{- 2 + 1} = {3}^{- 1} = 0.33$;
$x = - 1$ then $y = {3}^{- 1 + 1} = {3}^{0} = 1$;
$x = 0$ then $y = {3}^{0 + 1} = {3}^{1} = 3$;
$x = 1$ then $y = {3}^{1 + 1} = {3}^{2} = 9$;
$x = 2$ then $y = {3}^{2 + 1} = {3}^{3} = 27$;
Plotting these points you get: