math sec 4.6 rw

P x f x if q x is a rational function in lowest terms

Info iconThis preview shows page 1. Sign up to view the full content.

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

Unformatted text preview: nd the left. p( x) f ( x) = If q( x) is a rational function in lowest terms, then the line x = a is vertical asymptote to the graph of f(x) if and only if q(a) = 0 . Ex 2. Find the vertical asymptotes f ( x) = 15 x 2 − 3 x − 10 *factor the denominator So.. (x-5)(x+2) x=5, x=-2 <---- 2 vertical asymptotes 1. Make sure the function is in lowest terms 2. Factor or use quadratic formula 3. Set to y=0 to find vertical asymptotes Def: The line y = b is a horizontal asymptote for the graph of a rational function, f(x), if the value of f(x) approaches the value ‘b’ as x approaches ± ∞ . Ex. Consider the following function: x -10000 -4000 -2000 -1000 -500 0 500 1000 2000 4000 f(x) .7501 .7504 .7507 .7514 .7529 -.3333 .7471 .7486 .7493 .7496 Locating horizontal asymptotes: We want to look at the end behavior...
View Full Document

This document was uploaded on 11/13/2012.

Ask a homework question - tutors are online