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Domain and Asymptotes

Domain and Asymptotes. A rational function is a function of the form:. where p(x) and q(x) are polynomials. What would the domain of a rational function be?. We’d need to make sure the denominator  0. Find the domain. What would the domain of each rational function be?.

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Domain and Asymptotes

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  1. Domain and Asymptotes

  2. A rational function is a function of the form: where p(x)and q(x)are polynomials

  3. What would the domain of a rational function be? We’d need to make sure the denominator  0 Find the domain.

  4. What would the domain of each rational function be? • denominator  0

  5. Vertical Asymptotes The x-value(s) that we do not touch create vertical asymptotes.

  6. Vertical Asymptotes Vertical asymptotes are determined by the denominator of a rational function. There are vertical asymptotes at 3 and -6.

  7. Horizontal Asymptotes To find a horizontal asymptotes, we focus on the degree of the numerator and the denominator. What’s the degree? What’s the degree?

  8. How do we use degrees to find the horizontal asymptote? BOBO BOTN EATS DC

  9. BOBO Bigger On Bottom, y = O Degree of 3 Degree of 5 The degree is bigger on the bottom, so the horizontal asymptote is the line y = 0.

  10. BOTN Bigger On Top, No HA Degree of 6 Degree of 3 The degree is bigger on the top, so there is no horizontal asymptote.

  11. EATS DC Exponents Are The Same, Divide Coefficients Degree of 3 Degree of 3 The degrees are the same, so divide the leading coefficients. The horizontal asymptote is y = 2.

  12. Try it out!

  13. Quick Recap! Vertical Asymptote Horizontal Asymptote Find the degree of the numerator and denominator. Use BOBO BOTN EATS DC to find the horizontal asymptote. Use the denominator of the fraction. Determine what values of x make the denominator = 0.

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