Question

How do you find the domain and range of `g(x) = 5e^x`?

Answer 1

Domain: `(-oo,oo)` Range: `(0,oo)`

Explanation:

By default, the domain of the natural exponential function, or the values of `x` for which `f(x)=e^x` exists, is all real numbers, `(-oo,oo)`.

The range, unless the function is reflected across the `x`-axis by placing a negative sign in front of `e^x,` is `(0,oo).` This is because `e^x` can never equal zero (hence the open interval) and can never be negative -- these are fundamental properties of the exponential function. Furthermore, `e^x` increases as we plug in larger and larger values of `x,` it goes to infinity.

Here, our function involves no negative signs; thus, our range is `(0,oo).` The `5` has no impact on the range whatsoever.