# How do you find the vertical, horizontal and slant asymptotes of: y= 2^x?

Dec 18, 2017

This function has one asymptote at $y = 0$.

#### Explanation:

Any function of the form $y = {n}^{x}$, where $n$ is some number, has a horizontal asymptote where $y = 0$ because you can't raise a number to any power that will make that original number negative. Like, there is no $x$ that exists that could make ${n}^{x}$ a negative number.

Exponential functions have infinite domains, because there is no number you can put in for $x$ that would make $y = {2}^{x}$ not equal to a real number.
Since there are no $y$-values where the function can't exist, there is no horizontal or slant asymptote.

Note: You can also get the $y$-intercept by plugging $0$ in for $x$:
$y = {2}^{0} = 1$, so the $y$-intercept is at $\left(0 , 1\right)$.
Here's the graph: