# 9-2-1b - 2-1 Part II Graphing Rational Functions Six steps...

This preview shows pages 1–3. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 2-1 Part II: Graphing Rational Functions Six steps to pretty good graph of a rational function x−2 f ( x) = 2 Example: x −x 1. Factor numerator and denominator as much as possible. x−2 f ( x) = x ( x − 1) 2. Draw in vertical asymptotes (at zeros of denominator). zeros of denominator are 0 and 1. 3. Draw in horizontal asymptote (if any). degree of numerator < degree of denominator, so x-axis is horizontal asymptote. f(x) 10 vertical asymptotes horizontal asymptote x -3 2 2-1 Part II p. 1 4. Draw in zeros of function (zeros of numerator). x = 2 5. Add guide points between and beyond each zero and vertical asymptote. f(-2) = -2/3 f(1/2) = 6 f(3/2) = -2/3 f(3) = 1/6 guide points x X X -3 X X X 2 zero Note: there is one zero and two vertical asymptotes for a total of three. You will need 3 + 1 = 4 guide points. You always need one more guide point than the total of zeros and vertical asymptotes. And that should be enough to ensure a good-enough graph. 2-1 Part II p. 2 6. Draw. Make sure function approaches horizontal asymptote at left and right extremities. • start at extreme left • graph must enter from close to the horizontal asymptote there • or come from + or - oo, if no horizontal asymptote • will the graph start from above the asymptote or below the asymptote? • look at the left-most guide point for the clue • you must start on that side of the asymptote • now draw the graph through the left-most "in-between" point • graph must go off-scale at vertical asymptotes • it must never cross the x-axis except at marked zeros This can all be done with almost no algebra; just draw in some asymptotes and points and draw your graph! f(x) -3 10 2 2-1 Part II p. 3 ...
View Full Document

## This note was uploaded on 12/11/2011 for the course MATH 1324 taught by Professor Staff during the Spring '11 term at Austin Community College.

### Page1 / 3

9-2-1b - 2-1 Part II Graphing Rational Functions Six steps...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online