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# Precalculus Math 107

WSU

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This 4 page Class Notes was uploaded by Ashley Ernser II on Thursday September 17, 2015. The Class Notes belongs to Math 107 at Washington State University taught by Staff in Fall. Since its upload, it has received 16 views. For similar materials see /class/205967/math-107-washington-state-university in Mathematics (M) at Washington State University.

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Date Created: 09/17/15

MATH 107 7 Handout 36 1 Parent Function x x Rational Functions fx qx polynomial function Asymptotes are lines that our graphs approach Although these lines are not part of the graph ofa rational function they do serve as guidelines for the graph our function px polynomial function qx 0 Vertical Asym ptotes Form x If gt 00 or gt 00 as x gt a then you have the vertical asymptote x a To find the vertical asymptotes you set the denominator equal to zero and solve Horizontal Asym Etotes Formy If gt b as x gt 00 or x gt 00 then you have the horizontal asymptote y b To find the horizontal asymptote you first examine the degrees of the numerator and denominator leadin coe icient o x If the degrees are equal then the horizontal asymptote is y leading coef cient of qx If the degree is higher in the denominator then the horizontal asymptote is y 0 If the degree is higher in the numerator then there is no horizontal asymptote Slant Asym ptotes Form y mx b lfthe degree ofthe numerator is exactly one degree higher than the degree of the denominator then the function has a slant asymptote To find the slant asymptote use long division The slant asymptote is y Quotient do not include the remainder yintercegt 0 Setx 0 and solve xintercegt S 0 Sety 0 and solve Notice For rational functions Xintercept values are whatever turns the numerator into zero Helpful Points Choose xvalues surrounding the xvalues of the vertical asymptotes and the zeros to evaluate on a ttable y 2x 12 If W a Vertical Asymptotes b Horizontal Asymptote c yiintercept iiiiiiii if d xiintercepts iiiii Other helpful points x y Domain 2 gx a Vertical Asymptotes iiiiiiii if b Horizontal Asymptote 7 c y 7 intercept 77777 7 d x 7 intercepts 7777 Other helpful points x y D omain 3 Consider hx 2 25x 2 50 What is different about this function than the previous one How will the graph change x V a Vertical Asymptotes b Horizontal Asymptote 7 c y 7 intercept iiiiiiii d x 7 intercepts i Other helpful points x y Domain 2x2 5x712 439 x 2x1 a Vertical Asymptotes b Horizontal Asymptote iiiiiii if c Slant Asymptote iiiii if d y 7 intercept 77777 if e x 7 intercepts 7777 Other helpful points x y Domain 37x x6 5 gx a Vertical Asymptotes b Horizontal Asymptote 7 c y 7 intercept 7777777 d x 7 intercepts i Other helpful points x y Domain 2x2 4x 30 6 hx 7 H3 a Vertical Asymptotes b Horizontal Asymptote 7 c Slant Asymptote iiiii if d y 7 intercept iiiiii 7 e x 7 intercepts 7777 Other helpful points x y Domain 4x2 36 7 hx 2 2x 7x 9 a Vertical Asymptotes b Horizontal Asymptote iiiiiiiii W c Slant Asymptote iiiiiii d y 7 intercept iiiiiii e x 7 intercepts i Other helpful points x y Domain

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