Question

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

Answer 1

`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 oo`

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