College Algebra, Chapter 3, 3.1, Section 3.1, Problem 26

Evaluate the function $\displaystyle f(x) = \frac{|x|}{x}$ at $f(-2), \quad f(-1), \quad f(0), f(x^2),\quad f\left( \frac{1}{x} \right), \quad f(5)$
For $f(-2)$

$
\begin{equation}
\begin{aligned}
f(-2) &= \frac{|2|}{-2} && \text{Replace } x \text{ by } -2\\
\\
&= \frac{2}{-2} && \text{Simplify}\\
\\
&= -1
\end{aligned}
\end{equation}
$


For $f(-1)$

$
\begin{equation}
\begin{aligned}
f(-1) &= \frac{|-1|}{-1} && \text{Replace } x \text{ by } -1\\
\\
&= \frac{1}{-1} && \text{Simplify}\\
\\
&= -1
\end{aligned}
\end{equation}
$


For $f(0)$

$
\begin{equation}
\begin{aligned}
f(0) &= \frac{|0|}{0} && \text{Replace } x \text{ by } 0\\
\\
f(0) &= \text{Undefined}
\end{aligned}
\end{equation}
$


For $f(x^2)$

$
\begin{equation}
\begin{aligned}
f(x^2) &= \frac{|x^2|}{-2} && \text{Replace } x \text{ by } x^2\\
\\
&= \frac{x^2}{x^2} && \text{Simplify}\\
\\
&= 1
\end{aligned}
\end{equation}
$


For $f\left( \frac{1}{x} \right)$

$
\begin{equation}
\begin{aligned}
f\left( \frac{1}{x} \right) &= \frac{\left|\frac{1}{x}\right|}{\frac{1}{x}} && \text{Replace } x \text{ by } \frac{1}{x}\\
\\
&= x\left|\frac{1}{x}\right|
\end{aligned}
\end{equation}
$



For $f(5)$

$
\begin{equation}
\begin{aligned}
f(5) &= \frac{|5|}{5} && \text{Replace } x \text{ by }5\\
\\
&= \frac{5}{5} && \text{Simplify}\\
\\
&= 1
\end{aligned}
\end{equation}
$