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Published byMeghan Marsh Modified over 9 years ago
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A rational function is a function of the form: where p and q are polynomials
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What’s domain? The domain of a function is the set of all possible “input” values.
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We need to make sure the denominator 0 What can we NEVER divide by?!
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What’s the domain?
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Find the domain of Now, graph it! vertical asymptote! vertical asymptote!
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Asymptote An asymptote is a line that a curve approaches, but never touches!
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Find the domain of the following functions. Then graph them to find their vertical asymptotes. What do you notice about the domain of these functions and their asymptotes?
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Recap: How do we determine vertical asymptotes?
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Let’s take a look at the most recent example. Notice any other asymptotes? horizontal asymptote! horizontal asymptote!
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Horizontal Asymptotes To find a horizontal asymptotes, we focus on the degree of the numerator and the denominator. What’s the degree?
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How do we use degrees to find the horizontal asymptote?
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Degree of 3 Degree of 5 The degree is bigger on the bottom, so the horizontal asymptote is the line y = 0.
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Degree of 6 Degree of 3 The degree is bigger on the top, so there is no horizontal asymptote.
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Degree of 3 The degrees are the same, so divide the leading coefficients. The horizontal asymptote is y = 2.
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Find the horizontal asymptotes!
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Quick Recap! Vertical Asymptote Use the denominator of the fraction. Determine the values that make the denominator = 0. Horizontal Asymptote Find the degree of the numerator and denominator. Use BOBO BOTN EATS DC to find the horizontal asymptote.
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