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9.3 Rational Functions and Their Graphs Rational Function – A function that is written as, where P(x) and Q(x) are polynomial functions. The domain of f(x) is all real numbers except for those which Q(x) = 0. To find points of discontinuity, find the values of x that makes the denominator 0.

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Find the points of discontinuity for each rational function. Ex 1: Ex 2: Ex 3:

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Vertical Asymptotes and Holes -Both are types of discontinuity -Holes occur if there are common factors in the numerator and denominator -Vertical asymptotes occur when a factor in the denominator does not have a common factor in the numerator.

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Finding Vertical Asymptotes and Holes Ex 4: Ex 5:

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Finding Horizontal Asymptotes Three rules: 1.) If the degree of the denominator is larger than the degree of the numerator, then the horizontal asymptote is zero. 2.) If the degree of the denominator is smaller than the degree of the numerator, then there is no horizontal asymptote. 3.) If the degree of the denominator is equal to the degree of the numerator, then the horizontal asymptote is the quotient of the coefficients of the highest degree terms in the rational expression. Note: k values can change the value of an H.A in addition with these rules.

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Practice Problems Find the vertical asymptotes, holes, and horizontal asymptotes of each function if they exist. 1.)2.) 3.) 4.) 5.) 6.)

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