Question

Find the intercepts and asymptotes. (If an answer does not exist, enter DNE. Enter your asymptotes as a comma-separated list of equations if necessary.) r(x) = 5x^2 − 20x + 21 / x^2 − 4x + 4

x-intercept (x, y) =

y-intercept (x, y) =

vertical asymptote(s)

horizontal asymptote

Answer 1

Solution given that equation is 57?- 2031 +21 r(a) = 22 42 + 4 to find X-Intercept uee will put r(1)=y=o So, - 7101) 512 2071 +21 22 474 +4 0 = 5722- 2074 +21 22_44+4 522 203 +21 = 0 It is a quadratic equation, 932+ box +c=0 So, by the quadratic formula 2= -0 + / 62- 400 29 -|- 20) + / R9)”- 4 ( 5)(2) = 2X5 20 + 400 - 440 0 20+ - 20 25 10 So we can see here the value in the underoot is negetive so, here X - Intercept dorst not exist X - Intercept - DNE

For y - Intercept put d = 0 ola) = 51002- 2010) +21 (0)2- 4101 +4 y = 710) alt so, y - Intercept is 10,*) the ule will zero of to find vertical Asymptote denominator, so here r(1) = 5202 2034 +21 22 471+4 denominator zo 22 4x + 4 = 0 22- 201-23 + 4 = 0 a (2-2) – 2(2-2) = 0 (4-2) 171-2) = 0 (74-2)2=0 Vertical Hotel Msymptote 21 = 2 24 - 2 = 0 For Morizontal Asymptote, we will compare the degre of numerator and denominator, If degree is equal then Horizontal Asympto te will be

y = Coeffieclent of numerator of highest degree Corpfiuent of denominator of highest degree her degne of numerator is (2) equal to degna Of denominator is 12) Horizontal Asymptoto SO - ya vlor y = 5