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

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Presentation transcript:

A rational function is a function of the form: where p and q are polynomials

What’s domain? The domain of a function is the set of all possible “input” values.

We need to make sure the denominator  0 What can we NEVER divide by?!

What’s the domain?

Find the domain of Now, graph it! vertical asymptote! vertical asymptote!

Asymptote An asymptote is a line that a curve approaches, but never touches!

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?

Recap: How do we determine vertical asymptotes?

Let’s take a look at the most recent example. Notice any other asymptotes? horizontal asymptote! horizontal asymptote!

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

How do we use degrees to find the horizontal asymptote?

Degree of 3 Degree of 5 The degree is bigger on the bottom, so the horizontal asymptote is the line y = 0.

Degree of 6 Degree of 3 The degree is bigger on the top, so there is no horizontal asymptote.

Degree of 3 The degrees are the same, so divide the leading coefficients. The horizontal asymptote is y = 2.

Find the horizontal asymptotes!

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.