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NAME DATE PERIOD 373PracticeGraphs of Rational FunctionsSDetermine the equations of the vertical and horizontal asymptotes, if any, of each function. $4 2x ! 1 x !$ $3 1. (x) $2. (x) $3. G(x) $ 2Th
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How to fill out slant asymp graphs of

01
To fill out slant asymptote graphs, follow these steps: 1. Determine the slant asymptote equation. This can be done by dividing the numerator of the rational function by the denominator using long division or synthetic division. The quotient obtained will be the equation of the slant asymptote.
02
Plot the slant asymptote line on the graph. This line will be a straight line that approaches but never touches the graph of the rational function.
03
Determine the x-intercepts of the rational function. These are the points where the graph intersects the x-axis. To find these points, set the numerator of the rational function equal to zero and solve for x.
04
Determine the y-intercept of the rational function. This is the point where the graph intersects the y-axis. To find this point, set x equal to zero and solve for y.
05
Sketch the graph of the rational function by plotting additional points. Use the knowledge of the slant asymptote, x-intercepts, and y-intercept to determine the general shape of the graph. It is also helpful to determine the behavior of the rational function for large positive and negative values of x.
06
Connect the plotted points using a smooth curve that approaches the slant asymptote.

Who needs slant asymp graphs of?

01
Slant asymptote graphs are useful for anyone studying rational functions or analyzing their behavior. They are often used in calculus, algebra, and other mathematical fields. Students, teachers, and researchers can benefit from understanding how to fill out slant asymptote graphs as they provide valuable information about the behavior of rational functions.
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Slant asymptotes are diagonal lines that the graph of a rational function approaches as x goes to positive or negative infinity.
Anyone working with rational functions may need to understand and be able to identify slant asymptotes.
To find the slant asymptotes of a rational function, you can divide the numerator by the denominator and find the quotient with remainder.
Slant asymptotes help us understand the behavior of rational functions at the extremes of the x-axis.
The equations of the slant asymptotes and their corresponding behavior are important information to report.
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