Before graphing a given rational function, it is occasionally necessary to simplify it. If, other than at asymptotes, there are any excluded values then graphing the function requires an additional step.
The function y=f(x), where f(x) is a rational expression, is the formula for a rational function.
Drawing the graphs of the rational functions might be challenging. Finding the asymptotes and intercepts is a good place to start when attempting to sketch a graph of a rational function.
The steps in graphing rational functions are as follows:
Find the rational function's asymptotes, if any exist.
Create dotted lines for the asymptotes.
Find the rational function's x-intercept (s) and y-intercept, if any.
For various x values, determine the values of y.
Plot the spots and then create a straight line to connect them and check to see if the graph crosses the vertical asymptotes.
Make sure the function is not a continuous smooth curve at the excluded value if you want to portray an undefined function. Typically referred to as the "hole in the rational function," this excluded value
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