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Graphing Rational Functions

Graphing Rational Functions 1.9 - Solution

arrow_back Return to Graphing Rational Functions

To graph the given rational function, we will start by identifying the values of and We see above that and With this information, we will find the asymptotes and graph the function.

Asymptotes

Let's start by calculating the vertical asymptote. To do so, we need to solve the equation Since we already know the values of and we can substitute them in this equation and solve for
Solve for
The vertical asymptote is the line The horizontal asymptote is given by the equation Since we already know the values of and we will substitute them in this equation. The horizontal asymptote is the line

Graph

Let's make a table of values to find points on the curve. Make sure to include values of to the left and to the right of the vertical asymptote.

Let's plot and connect the obtained points. Keep in mind that rational functions have two branches. Do not forget to graph the asymptotes!