Question

In Problems $97-100$, graph each function. Based on the graph, state the domain and the range and find any intercepts.

$f\left(x\right)=\left\{\begin{array}{l}{e}^{-x}ifx<0\\ e^{x}ifx\ge 0\end{array}\right.$

Short answer

The domain of the given function is$(-\infty ,\infty )$and its range is$[1,\infty )$and intercept is$(0,1)$.

Step-by-step solution

Step 1. The graph of given function is 

Step 2. The domain and range of the function.

The graph of $e^{-x}$for $x<0$ consists of only those values of x that are negative and the graph of $e^x$for $x\ge 0$ consists of only those values of x that are positive.

From the graph, it can be concluded that the domain of the function is$(-\infty ,\infty )$and the range of the function is$\{x;x\ge 1\}$or$[1,\infty )$. The intercept for the given function is$(0,1)$.