# What is the domain and range of y =2^x?

Jan 7, 2018

color(red)("Domain" - x in RR

color(blue)("Range" - y > 0

#### Explanation:

Finding the domain:

We must ask what values of $x$ yields a valid value of $y$, and since this is just a simple exponential function, all values of $x$ gives you a real value of $y$

color(red)("Domain" - x in RR

Now we must consider the range, so what are the values that $y$ could possiblally take on, with a sketch we can see:

graph{y = 2^x [-9.83, 10.17, -1.2, 8.8]}

We see that all possitive values of $y$ can be obtained, but not $y = 0$ as this is the functions asymptotoe, and occurs as $x \to \infty$

color(blue)("Range" - y > 0