Rational Functions A rational function has the form

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Presentation transcript:

Rational Functions A rational function has the form where P and Q are polynomial functions and . Ex 1: Examine Note: also

The line x = a is a vertical asymptote of the function if The line y = b is a horizontal asymptote of the function if

Ex 2: Graph

Ex 3: Graph

Let r be the rational function The vertical asymptotes of r are the lines x = a, where a is a zero of the denominator. 2. (a) If n < m, then r has a horizontal asymptote y = 0. (b) If n = m, then r has a horizontal asymptote (c) If n > m, then r has no horizontal asymptote.

Ex 4: Find the asymptotes of

Graphing Rational Functions Factor the numerator and denominator. 2. Find the x-intercepts and y-intercept. 3. Find the vertical asymptotes (if any). 4. Find the horizontal asymptote (if any). 5. Make a small T-chart. 6. Sketch the graph.

Ex 5: Graph

Ex 6: Graph

Ex 7: Graph

A slant asymptote is a diagonal line that the graph A slant asymptote is a diagonal line that the graph of a function approaches as . A slant asymptote occurs when the degree of the numerator is one more than the degree of the denominator. We calculate a slant asymptote by dividing the numerator by the denominator and ignoring the remainder.

Ex 8: Graph

Ex 9: Graph

Assignment S 4.5: pg 369 - 370 #7-10,16,21-24,40,42,43,54,55