What is the range of y=3^x

The range of this function is y is equal to all real numbers such that y > 0.

We know this because of the behavior of this graph. As the numbers get larger and larger, so does the f (x) value. See below.

f (x) = 3^x

f (1) = 3^1

f (1) = 3

f (4) = 3^4

f (4) = 81

This means there is no restriction on how high they go.

As for how low they go, the numbers will get increasingly close to 0, but never reach it (also known as a limit). See a couple examples below.

f (-2) = 3^-2

f (-2) = 1/9

f (-5) = 3^-5

f (-5) = 1/243

You'll notice that there is no value that will result in a 0 or negative number, giving us the range above.