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3.4 Rational Functions I.

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Presentation on theme: "3.4 Rational Functions I."— Presentation transcript:

1 3.4 Rational Functions I

2 A rational function is a function of the form
Where p and q are polynomial functions and q is not the zero polynomial. The domain consists of all real numbers except those for which the denominator is 0.

3 Find the domain of the following rational functions:
All real numbers except -6 and-2. All real numbers except -4 and 4. All real numbers.

4

5 y Horizontal Asymptotes y = R(x) y = L x y y = L x y = R(x)

6 Vertical Asymptotes x = c y x x = c y x

7 If an asymptote is neither horizontal nor vertical it is called oblique.
x

8 Theorem Locating Vertical Asymptotes
A rational function In lowest terms, will have a vertical asymptote x = r, if x - r is a factor of the denominator q.

9 Vertical asymptotes: x = -1 and x = 1
Find the vertical asymptotes, if any, of the graph of each rational function. Vertical asymptotes: x = -1 and x = 1 No vertical asymptotes Vertical asymptote: x = -4

10 Consider the rational function
1. If n < m, then y = 0 is a horizontal asymptote of the graph of R. 2. If n = m, then y = an / bm is a horizontal asymptote of the graph of R. 3. If n = m + 1, then y = ax + b is an oblique asymptote of the graph of R. Found using long division. 4. If n > m + 1, the graph of R has neither a horizontal nor oblique asymptote. End behavior found using long division.

11 Find the horizontal and oblique asymptotes if any, of the graph of
Horizontal asymptote: y = 0 Horizontal asymptote: y = 2/3

12 Oblique asymptote: y = x + 6


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