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Solving and Graphing Rational Equations
Before we start, let's review the significance of the domain of a rational function.
Remember, the denominator cannot equal zero.
This restriction will be important as we find solutions to rational functions.
This restriction will be a point as we set up our number line and include some test values.
View the following presentation before the next video. Click on the pointing finger to see the interactive elements (audio).
Graph of Rational Function - Example 1
The graph of the rational function is attached below.
Compare the number line analysis (above) to the actual graph.
Intervals
~ (-∞, -5) region is positive, therefore, the graph is above the x-axis and "hugs" the vertical asymptote at x = -5.
Notice the graph does NOT cross the x-axis. It "hugs" the horizontal asymptote y = 0.
~ (-5, -3) region is positive, therefore, the graph is above the x-axis and "hugs" the vertical asymptote at x = -3.
This graph will cross the x-axis because of the zero at x = -1.
~ (-1, 1) region is negative, therefore, the graph is below the x-axis.
Zooming in (insert), we see the graph is below the x-axis.
~ (1, ∞) region is positive, therefore, the graph is above the x-axis and "hugs" the horizontal asymptote y = 0.
This graph will cross the x-axis because of the zero at x = 1.
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