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
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.