Difference between revisions of "Graph a Rational Function"
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A rational function is an equation that takes the form ''y'' = N(''x'')/D(''x'') where N and D are polynomials. Attempting to sketch an accurate graph of one by hand can be a comprehensive review of many of the most important high school math topics from basic algebra to differential calculus. Consider the following example: ''y'' = (2''x''<sup>2</sup> - 6''x'' + 5)/(4''x'' + 2). | A rational function is an equation that takes the form ''y'' = N(''x'')/D(''x'') where N and D are polynomials. Attempting to sketch an accurate graph of one by hand can be a comprehensive review of many of the most important high school math topics from basic algebra to differential calculus. Consider the following example: ''y'' = (2''x''<sup>2</sup> - 6''x'' + 5)/(4''x'' + 2). | ||
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== Steps == | == Steps == | ||
#'''Find the ''y'' intercept.''' Simply set ''x'' = 0. Everything but the constant terms vanish, leaving ''y'' = 5/2. Expressing this as a coordinate pair, (0, 5/2) is a point on the graph. [[Graph Points on the Coordinate Plane|Graph that point]]. | #'''Find the ''y'' intercept.''' Simply set ''x'' = 0. Everything but the constant terms vanish, leaving ''y'' = 5/2. Expressing this as a coordinate pair, (0, 5/2) is a point on the graph. [[Graph Points on the Coordinate Plane|Graph that point]]. | ||
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#'''Connect the dots''' and smoothly extend the graph from the known points to the asymptotes taking care to approach them from the correct direction. Take care not to cross the ''x''-axis except at the points already found in step 3. Don't cross the horizontal or linear asymptote except at the points already found in step 5. Don't change from upward sloping to downward sloping except at the extreme found in the previous step. | #'''Connect the dots''' and smoothly extend the graph from the known points to the asymptotes taking care to approach them from the correct direction. Take care not to cross the ''x''-axis except at the points already found in step 3. Don't cross the horizontal or linear asymptote except at the points already found in step 5. Don't change from upward sloping to downward sloping except at the extreme found in the previous step. | ||
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== Tips == | == Tips == | ||
