\begin{frame} \frametitle{1st Midterm Exam - Review} \begin{exampleblock}{} Express the domain of the function \begin{talign} f(x) = \frac{x + \log (x+1) + \sqrt{5-x}}{x-2} \end{talign} as a union of intervals. \pause\medskip We analyze the parts: \begin{itemize} \pause \item $\log (x+1)$ is defined for \pause $x > -1$, thus $(-1,\infty)$ \pause \item $\sqrt{5-x}$ is defined on $x \le 5$, thus $(-\infty,5]$ \pause \item the fraction $\frac{\ldots}{x-2}$ is defined for \pause$x\ne 2$, thus $(-\infty,2) \cup (2,\infty)$ \end{itemize} \pause\medskip \alert{The domain of $f$ is not: \begin{talign} (-1,\infty) \cup (-\infty,5] \cup (-\infty,2) \cup (2,\infty) \mpause[1]{\quad=\quad (-\infty,\infty)} \end{talign}} \pause\pause The domain of $f$ is: \begin{talign} (-1,2) \cup (2,5] \end{talign} \end{exampleblock} \end{frame}