Question

What is the domain and range of `f(x) =e^x`?

Answer 1

See below.

Explanation:

`f(x)=e^x`

This function is valid for all real `x`, so the domain is:

`color(blue)({x in RR}`

Or in interval notation:

`color(blue)((-oo,oo)`

To find the range we observe what happens as `x` approaches `+-oo`

as: `x->oo` , `color(white)(8888)e^x->oo`

as: `x->-oo` , `color(white)(8888)e^x->0`

( i.e if x is negative we have `bb(1/(e^x)`)

We also observe that `e^x` can never equal zero.

So our range is:

`color(blue)({f(x) in RR | 0 < x}`

Or

`color(blue)((0,oo)`

This is confirmed by the graph of `f(x)=e^x`

graph{y=e^x [-16.02, 16.01, -8.01, 8.01]}