Graphing Rational Functions
Main Concept

To graph a rational function, it is useful to follow these steps:
1.

Plot all asymptotes  vertical, horizontal and oblique.

2.

Plot $x$ and $y$intercepts.

3.

Plot several points, both close to and far from vertical asymptotes. If there are some areas in which the behavior of the function is unclear, plot more points.

4.

Connect the points with smooth lines. Remember that vertical asymptotes cannot be crossed, but horizontal and oblique ones can be.




Generate a rational function and try to draw it on the graph. Use the radio buttons below the graph to graph different elements in different colors. When you are finished, click the corresponding check boxes to see how accurate you were.
${}$


$f\left(x\right)\=$

Show:








Draw:

${}$



${}$

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