Q. 97 - Precalculus Enhanced with Graphing Utilities

Question

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

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

Step-by-Step Solution

Answer

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

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 $(0,1)$.