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

Mar 2, 2018

Domain: $\left(- \infty , \infty\right)$ Range: $\left(0 , \infty\right)$
By default, the domain of the natural exponential function, or the values of $x$ for which $f \left(x\right) = {e}^{x}$ exists, is all real numbers, $\left(- \infty , \infty\right)$.
The range, unless the function is reflected across the $x$-axis by placing a negative sign in front of ${e}^{x} ,$ is $\left(0 , \infty\right) .$ 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 $\left(0 , \infty\right) .$ The $5$ has no impact on the range whatsoever.