# How do you graph: y = 2^x + 2?

Mar 15, 2018

Look at the explanation for this is a "how" question.

#### Explanation:

First you have to know how the equation $y = {a}^{x}$ looks.
It looks like this:
graph{1.5^x [-83.3, 83.35, -41.66, 41.65]}
That is the general shape.

The range of every equation for $y = {a}^{x}$ is $\left(0 , \infty\right)$
Also the point $\left(0 , 1\right)$ exists on every exponential function because ${a}^{0} = 1$
Also there is always a horizontal asymptote at $y = 0$ unless there is a vertical shift, then it moves up or down.

Now plug in some points
$x = - 1 , y = 0.5$
$x = 1 , y = 2$
$x = 2 , y = 4$

Now you just shift the whole graph up by 2
This makes the horizontal asymptote at $y = 2$
graph{2^x+2 [-83.3, 83.35, -41.66, 41.65]}