"Rational Functions: Graphing, Domains, Asymptotes, and Holes"
Learn how to identify and evaluate rational functions, graph them, find their domains, write equations for their asymptotes, and spot any holes in their graph. Understand important terms like excluded values, horizontal and vertical asymptotes, rational expressions, and rational functions.
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About "Rational Functions: Graphing, Domains, Asymptotes, and Holes"
PowerPoint presentation about '"Rational Functions: Graphing, Domains, Asymptotes, and Holes"'. This presentation describes the topic on Learn how to identify and evaluate rational functions, graph them, find their domains, write equations for their asymptotes, and spot any holes in their graph. Understand important terms like excluded values, horizontal and vertical asymptotes, rational expressions, and rational functions.. The key topics included in this slideshow are . Download this presentation absolutely free.
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1. Copyright by Holt, Rinehart and Winston. All Rights Reserved. Objectives Identify and evaluate rational functions. Graph a rational function, find its domain, write equations for its asymptotes, and identify any holes in its graph. 8.2 Rational Functions and Their Graphs
2. Copyright by Holt, Rinehart and Winston. All Rights Reserved. Glossary Terms excluded values hole in the graph horizontal asymptote rational expression rational function vertical asymptote 8.2 Rational Functions and Their Graphs
3. Copyright by Holt, Rinehart and Winston. All Rights Reserved. Rules and Properties Vertical Asymptote 8.2 Rational Functions and Their Graphs In a rational function R , if x a is a factor of the denominator but not a factor of the numerator, x = a is vertical asymptote of the graph of R .
4. Copyright by Holt, Rinehart and Winston. All Rights Reserved. Rules and Properties Horizontal Asymptote 8.2 Rational Functions and Their Graphs If degree of P < degree of Q , then the horizontal asymptote of R is y = 0. R ( x ) = is a rational function; P and Q are polynomials P Q If degree of P = degree of Q and a and b are the leading coefficients of P and Q , then the horizontal asymptote of R is y = . a b
5. Copyright by Holt, Rinehart and Winston. All Rights Reserved. Rules and Properties Horizontal Asymptote 8.2 Rational Functions and Their Graphs If degree of P > degree of Q , then there is no horizontal asymptote R ( x ) = is a rational function; P and Q are polynomials P Q
6. Copyright by Holt, Rinehart and Winston. All Rights Reserved. Rules and Properties Hole in the Graph 8.2 Rational Functions and Their Graphs In a rational function R , if x b is a factor of the numerator and the denominator, there is a hole in the graph of R when x = b (unless x = b is a vertical asymptote).
7. Copyright by Holt, Rinehart and Winston. All Rights Reserved. Key Skills Identify all excluded values, asymptotes, and holes in the graph of a rational function. 8.2 Rational Functions and Their Graphs f ( x ) = 2 x 2 + 2 x x 2 1 factor: f ( x ) = 2 x ( x + 1) ( x + 1)( x 1)
8. Copyright by Holt, Rinehart and Winston. All Rights Reserved. Key Skills Identify all excluded values, asymptotes, and holes in the graph of a rational function. 8.2 Rational Functions and Their Graphs excluded values: x = 1 and x = 1 hole in the graph: x = 1 vertical asymptote: x = 1 horizontal asymptote: y = 2 TOC
