Question

Analyze and sketch a graph of the function. Find any intercepts, relative extrema, points of infection, and asymptotes. (If an answer does not exist, enter DNE.) Rx) xvx intercept (x, y) (smaller x-value) (targer x-value) relative minimum )- relative maximum (X) = point of Inflection (x,y) = Find the equation of the asymptote. Use a graphing utility to verify your results. 6 Web 4

Answer 1

- is FO) f(x)= anret. then - Hoizontal and vertical asymptote: Let rational function ta; se't a bmame tbi&tbo vertical asyroptotes at those values of for which denominatoo is equed to Zero. Horizontal asymptote? (i) if then Ciin pf man, an Hot bo Chri) man then f(a) doesn't have him * 호 msn, y=o is HoA thes = is if

f(x)= x 55 x Gives function put y=00 f(2)=0 To know x-intercept 09) O= se sc Tor co 15 5-x xro 602 x-520 2-5 so x intercept is 00) & (5,0) To know yrintercept put xao foro 85-0 fCoro y-intercept $ 0,0) (ii) Differentiate f(x) and equate to zero f(x)= d de (x x5-x) = C') 15-x ta (-1) 2V5 fCH 25-x) 2 a 2 2 15* f'(x)20 a 10-ax de - o 255-n znalo x 3 TO know Whether it gives maximum value (or minimum value. find F"(x) f"(%) = 2 r (f'(as) = 10-3u ( dre 2 √5-x

(-1) 2 55-1 19 NI -3Cu) (15-x)-(10-30 Crem) 6 C5-x) + 10.-3% 2. G-x) 15+ ul - ام 30 +62 +10-31 pla 2 (5 x 34 3x - 20 z 호 2C5-x) To f"( * )= C 3620 205-03 13 4 2(3 since f" () co. at maxima. x2 cul f(x) has local elm since f(3) = 0 5- 1 4:3033 f(w) doesn't have relative mininia and . Point of inflection points. Horizontal asymptote: fra) doesn't have denominator portion of x BCA) doesn't have Horizontal asymptote vertical asymptote? since numerator = gree er than degree of desommator=o. so f(x) doesn't have vertical asymptote Degree of It's si iş

f(n) Domain of Domain of iv 5x yo aso ra So · Domain of F(x) $ of f(x) rs. C- 3) (19) 4303 -aseş 6,0) y=x15 ly . Yanış 02 intercept 2,4)=60) 4)=(5,0) on relative relative minima relative maxi point of inflections air) Asymptote - NA option "b iş correct. mce Cc, f)= NA (x,y)= (x,y) = (1939, 4-303 = NA +

If you have any doubt leave a comment