Graphing Rational Functions

Introduction

For now we mention the 7 steps to analyze the graph of a rational function. In the future there will be pictures to accompany the steps

Analyzing the graph of a rational function

Let R be the rational function we want to graph.

 Step 1: Factor the numerator and denominator of R. Note the domain of the rational function

 Step 2: Write R in lowest terms.

 Step 3: Find the x and y-intercepts. Plot them.

 Step 4: Find the vertical asymptotes and graph then using dashed lines. 

 Step 5: Find the horizontal asymptote,  if one exists. Find points, if any, at which the graph intersects the asymptote.
 Graph the asymptote as a horizontal dashed line. Plot any points at which the graph intersects the asymptote.

 Step 6: Use the zeros and vertical asymptotes to divide the x-axis into intervals. Determine if the function is positive or negative
 in each of these     intervals,
 by evaluating the function at one point in each interval.

 Step 7: Use the results from the previous steps to graph R.

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