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Asymptotes and Holes Graphing Rational Functions

Asymptotes and Holes Graphing Rational Functions

online.math.uh.edu

Exercise Set 2.3: Rational Functions MATH 1330 Precalculus 229 Recall from Section 1.2 that an even function is symmetric with respect to the y-axis, and an odd function is symmetric with respect to the origin. This can sometimes save time in graphing rational functions. If a function is even or odd, then half of the function can be

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Asymptotes, Holes, and Graphing Rational Functions

Asymptotes, Holes, and Graphing Rational Functions

www.sctcc.edu

Asymptotes, Holes, and Graphing Rational Functions Holes It is possible to have holes in the graph of a rational function. Before putting the rational function into lowest terms, factor the numerator and denominator. If there is the same factor in the numerator and denominator, there is a hole. Set this factor equal to zero and solve. The

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4.4: Graphing Rational Functions Practice Date Period

4.4: Graphing Rational Functions Practice Date Period

www.birmingham.k12.mi.us

4.4: Graphing Rational Functions Practice Identify the holes, vertical asymptotes, x-intercepts, horizontal asymptote, and domain of each. Then sketch the graph. 1) f (x) = 4 x − 3 x y −8 −6 −4 −2 2 4 6 8 −8 −6 −4 −2 2 4 6 8 2) f (x) = x2 + 7x + 12 −2x2 − 2x + 12 x y −8 −6 −4 −2 2 4 6 8 −8 −6 −4 −2 2 4 6 8 ...

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GRAPHING RATIONAL FUNCTIONS

GRAPHING RATIONAL FUNCTIONS

www.cbsd.org

GRAPHING RATIONAL FUNCTIONS To Identify Types of Discontinuity: Step 1: HOLES (Removable Discontinuities) Factor numerator & denominator Simplify If anything cancels, then there is a hole (More than one factor cancels More than one hole) Find the ordered pair, ( , ), substitute x into the SIMPLIFIED EQUATION to get y

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Graphing Rational Functions.ks-ia2 - cdn.kutasoftware.com

Graphing Rational Functions.ks-ia2 - cdn.kutasoftware.com

cdn.kutasoftware.com

Graphing Rational Functions Date_____ Period____ Identify the points of discontinuity, holes, vertical asymptotes, x-intercepts, and horizontal asymptote of each. 1) f ( x) = x x Discontinuities: , Vertical Asym.: x , x Holes: None Horz. Asym.: y

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Rational Expressions Worksheet

Rational Expressions Worksheet

math.gmu.edu

2. Simplify 2 2 2 9 4 3 x x x x 3. Simplify 2 3 1 3 x 4. Simplify 1 1 x y y x Graphing Rational Functions 1. Graph each equation. a. 1 y x y b. 1 x 2. Graph each equation.

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Graphing Rational Functions.ks-ia2 - Kuta Software LLC

Graphing Rational Functions.ks-ia2 - Kuta Software LLC

www.kutasoftware.com

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