Properties of Rational Functions Dr. Fowler AFM Unit 3-2 Properties of Rational Functions
Finding the Domain of any Function: WATCH VIDEO: Finding the Domain of any Function: https://www.youtube.com/watch?v=hZEGZMb4uzQ
3.6: Rational Functions and Their Graphs Rational functions are quotients of polynomial functions. This means that rational functions can be expressed as where p(x) and q(x) are polynomial functions and q(x) 0. The domain of a rational function is the set of all real numbers except the x-values that make the denominator zero. For example, the domain of the rational function is the set of all real numbers except 0, 2, and -5. This is p(x). This is q(x).
EXAMPLE: Finding the Domain of a Rational Function 3.6: Rational Functions and Their Graphs EXAMPLE: Finding the Domain of a Rational Function Find the domain of each rational function. a. Solution Rational functions contain division. Because division by 0 is undefined, we must exclude from the domain of each function values of x that cause the polynomial function in the denominator to be 0. a. The denominator of is 0 if x = 3. Thus, x cannot equal 3. The domain of f consists of all real numbers except 3, written {x | x 3}. more
EXAMPLE: Finding the Domain of a Rational Function 3.6: Rational Functions and Their Graphs EXAMPLE: Finding the Domain of a Rational Function Find the domain of each rational function. a. Solution Rational functions contain division. Because division by 0 is undefined, we must exclude from the domain of each function values of x that cause the polynomial function in the denominator to be 0. b. The denominator of is 0 if x = -3 or x = 3. Thus, the domain of g consists of all real numbers except -3 and 3, written {x | x - {x | x -3, x 3}. more
EXAMPLE: Finding the Domain of a Rational Function 3.6: Rational Functions and Their Graphs EXAMPLE: Finding the Domain of a Rational Function Find the domain of each rational function. a. Solution Rational functions contain division. Because division by 0 is undefined, we must exclude from the domain of each function values of x that cause the polynomial function in the denominator to be 0. c. No real numbers cause the denominator of to equal zero. The domain of h consists of all real numbers.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Oblique Asymptote a.k.a. “Slant” Asymptote Horizontal Asymptote Vertical Asymptote A vertical asymptote is a vertical line that doesn't intersect the graph of the function.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Excellent Job !!! Well Done