Answer
$$\eqalign{
& \left( {\text{a}} \right){\text{ Discontinuity at }}x = 2 \cr
& \left( {\text{b}} \right){\text{Increasing: }}\left( { - \infty ,2} \right),\left( {2,\infty } \right) \cr
& \left( {\text{c}} \right){\text{No relative extrema}} \cr} $$
Work Step by Step
$$\eqalign{
& f\left( x \right) = \frac{{{x^2} - 3x - 4}}{{x - 2}} \cr
& \left( {\text{a}} \right){\text{Calculating the first derivative}} \cr
& f'\left( x \right) = \frac{d}{{dx}}\left[ {\frac{{{x^2} - 3x - 4}}{{x - 2}}} \right] \cr
& f'\left( x \right) = \frac{{\left( {x - 2} \right)\left( {2x - 3} \right) - \left( {{x^2} - 3x - 4} \right)}}{{{{\left( {x - 2} \right)}^2}}} \cr
& f'\left( x \right) = \frac{{2{x^2} - 3x - 4x + 6 - {x^2} + 3x + 4}}{{{{\left( {x - 2} \right)}^2}}} \cr
& f'\left( x \right) = \frac{{{x^2} - 4x + 10}}{{{{\left( {x - 2} \right)}^2}}} \cr
& {\text{Calculating the critical points, set }}f'\left( x \right) = 0 \cr
& {x^2} - 4x + 10 = 0 \cr
& x = \frac{{ - \left( { - 4} \right) \pm \sqrt {{{\left( { - 4} \right)}^2} - 4\left( 1 \right)\left( {10} \right)} }}{{2\left( 1 \right)}} \cr
& x = \frac{{4 \pm \sqrt {16 - 40} }}{2} \cr
& {\text{No real solutions}} \cr
& {\text{There are no values at which }}f'\left( x \right) = 0:{\text{ No relative extrema}} \cr
& {\text{The derivative is not defined at }}x = - 2,{\text{ so the critical}} \cr
& {\text{point is }}x = 2 \cr
& \left( {\text{b}} \right){\text{Set the intervals }}\left( { - \infty ,2} \right),\left( {2,\infty } \right) \cr
& {\text{Making a table of values }}\left( {{\text{See examples on page 180 }}} \right) \cr} $$
\[\begin{array}{*{20}{c}}
{{\text{Interval}}}&{\left( { - \infty ,2} \right)}&{\left( {2,\infty } \right)} \\
{{\text{Test Value}}}&{x = - 4}&{x = 4} \\
{{\text{Sign of }}f'\left( x \right)}&{{\text{ }}f'\left( { - 4} \right) = \frac{7}{6} > 0}&{{\text{ }}f'\left( 4 \right) = \frac{5}{2} > 0} \\
{{\text{Conclusion}}}&{{\text{Increasing}}}&{{\text{Increasing}}}
\end{array}\]
$$\eqalign{
& \left( {\text{c}} \right){\text{ No relative extrema because there are no values at which}} \cr
& f'\left( x \right) = 0 \cr
& \cr
& \left( {\text{d}} \right){\text{Graph}} \cr} $$
