Difference between revisions of "Graphing Rational Functions"
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(Created page with "<div class="noautonum">__TOC__</div> ==Introduction== For now we mention the 7 steps to analyze the graph of a rational function. In the future there will be pictures to acco...") |
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==Analyzing the graph of a rational function== | ==Analyzing the graph of a rational function== | ||
| − | Step 1: Factor the numerator and denominator of R. Note the domain of the 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 2: Write R in lowest terms. |
| − | Step 3: Find the x and y-intercepts. Plot them. | + | Step 3: Find the x and y-intercepts. Plot them. |
| − | Step 4: Find the vertical asymptotes and graph then using dashed lines. | + | 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. | + | 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. | + | 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, | + | 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. | + | by evaluating the function at one point in each interval. |
Step 7: Use the results from the previous steps to graph R. | Step 7: Use the results from the previous steps to graph R. | ||
[[Math_5|'''Return to Topics Page]] | [[Math_5|'''Return to Topics Page]] | ||
Revision as of 07:25, 21 October 2015
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.