5.2-3 RationalFunctions

5.2-3 RationalFunctions - Find the domain and any vertical,...

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5.2: RATIONAL FUNCTIONS A rational function R(x) is a quotient of two polynomials p(x)/q(x) where q is not the zero polynomial. The domain consists of all real numbers except those for which the denominator q = 0. An asymptote is a line to which a certain part of the graph of a function gets closer and closer but never touches. A rational function in lowest terms will have a vertical asymptote at any value of x that would cause the denominator to equal zero. Proper rational functions, where the degree of the numerator is less than that of the denominator, will have a horizontal asymptote at y = 0 . If the degree of the numerator is greater than or equal to that of the denominator, the horizontal or oblique asymptote can be found by long division; it will be the quotient without the remainder. The real zeros of a rational function are the values for which p(x) = 0.
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Unformatted text preview: Find the domain and any vertical, horizontal asymptotes: Domain Asymptotes Zeros 1. f x x x x ( ) ( ) ( ) =--+ + 2 4 3 4 4 2 2 2. 2 3 2 2 2 ( ) 2 4 x x f x x x-+ = + 3. 2 2 6 12 ( ) 3 5 2 x x f x x x + + =--Graph using transformations: 4. ( 29 R x x = 2 1 5. ( 29 ( 29 R x x = + 2 1 2 6. ( 29 ( 29 R x x = + + 2 1 2 2 7. ( 29 ( 29 R x x-= + + 2 1 2 2 5.3 Rational Functions II: Analyzing Graphs 1. ( 29 2 2 9 x R x x-=-2. ( 29 2 2 8 26 15 2 15 x x R x x x + + =--Asymptotes: Vertical Horizontal Real zeros: Other Points: 3. Find an equation for the graph below: TRY THESE Find the domain and any vertical, horizontal, or oblique asymptotes, and the real zeros & graph: Domain Asymptotes Zeros 4. 2 2 6( 4) ( ) 3( 4 4) x f x x x--= + + = 5. 2 3 2 8 8 ( ) 4 x f x x x-+ = + 6. 2 5 4 ( ) 4 2 x x f x x-+ = +...
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This note was uploaded on 01/04/2012 for the course MAC 1105 taught by Professor Staff during the Fall '08 term at Miami Dade College, Miami.

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5.2-3 RationalFunctions - Find the domain and any vertical,...

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