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Graphing rational functions
Lesson 78 Graphing rational functions
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Rational function A rational function is a function whose rule can be given as a rational expression. This means that a rational expression has a variable in the denominator- they are undefined when the denominator is equal to zero. A value of a variable for which an expression or a function is undefined is called an excluded value.
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Find the excluded values
y= m-4 3m-12 Simplify the denominator by factoring out GCF 3(m-4) Set the denominator equal to 0, to find the excluded value 3(m-4)= 0 m-4 = 0 m= 4 is the excluded value
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Find the excluded values
2 x-8 4 x+10
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Discontinuous functions
Rational functions are discontinuous functions. Discontinuous functions are functions that have a break or jump in the graph. A break or jump in the graph can be due to an asymptote. An asymptote is a boundary line that the graph of a function approaches but never touches or crosses
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Vertical asymptote To determine vertical asymptotes, find the excluded value for the function
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Horizontal asymptotes
Rational functions also have horizontal asymptotes. When the function is in the form y= a c x-b the horizontal asymptote is at y = c When c = 0, the horizontal asymptote is the x-axis
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Identify the asymptotes
x-8 to find vertical asymptote , find excluded value x-8 = 0, so x = 8 is vertical asymptote since c= 0 , the horizontal asymptote is y = 0
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Identify the asymptotes
x+10 y = 5 x-1 y= x-3
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Graphing using asymptotes
The parent function for rational functions is y= 1 x By identifying the asymptotes and graphing them with dotted lines, and plotting a few points, the rational function can be graphed.
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Identify the asymptote and graph
x vertical asymptote is x = 4 horizontal asymptote is y = -2 Graph the asymptotes as dotted lines Make a table of values (choose points on either side of the vertical asymptote) x y /4 -5/ /2 Plot the points and connect them with smooth curves
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Identify the asymptotes and graph
x-3 y = x+2
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