Question

COLLEGE sity of New York YCS & COMPUTER SCIEN Sing=1 CC BY * Sec (x1" 4. (10 points) Let g(r) = 2.13 - 9.1? + 3x + 4 a List all possible rational roots of according to the Rational Zeros Theorem (b) Factor g completely: (c) Ther-intercepts of the graph of y=g() are: (d) The y-intercept of the graph of y=g() is: (e) Sketch the graph of y = g(ur) in the axes below. + - (1 + 1)(1 - 1) <0. SO. 5. (10 points) Solve the inequality - (I - 2)²

Answer 1

Given that gras - 2 4 -qx+3x+4 19 -9 3 + 239 + 3x + 4 = 0 SG (2X-7X-4) 2 o 2 -1 -4 -. To Icoop2-72--0 2x²7x-4 = 0 x = 7 5 49-4.2.1-4) - 2.2 = 7 ± √49+32 4 =74fET = 7 =747,7 *): 6 -1) (2-4) (17+) -0 =4,5 tince the rational 4 x-intercepts are A) Y - intercepts s roots of gow are 1,4 and a ( 33,0), (1,0) and (4,0). (0,4). * x. intercepts Y- inte 19,4 Hot- 23 Graph of g(x) .

Given inequality is (x+1)(x-4) (arz) (2+1) (9-4) = 0 o and at I c x-4 to x<-1 and x> 4 af1>o and x-4 co a> -1 and na 4. xtiro ad 2-4 = 0 * X=- ad =4. a sol and x x 4 (or) «?-1 ad x 4 , is 6 Given that fee) = (-u) (x+2) (x+4) (x-1) x-intercept are obtained by equating (x-4) (x+2) = 0 ix-uto or xt2 = x=u und wird ..x- intercepts are (4,0) and (-2,0). - intacepts are is (0,2)) I

Jim" * -x-intercept o-y-intercept 0 13 (4,0) . tim tex) = xt-4t [xtu) (x-1) Graph of fex). * line x=L is a vertical asymptote of the function = fend, it the limit of the dunction at this point in intinite. The function fox) og undefined est n=-4 and a=1 - at (2-4) (x+2) = -8 (-2) = D. xt-4t 01-5) et (-u) (i+2) = D. xalt Tiny) (1.1) x=-4 and x=1 are the vertical asymptotes of tens = (2-4) (x+2) Tatu) (x-1). The line of ya feat yol is a honizontal asymptote it either sim ten = L or sem fex) =L, (Listinite) dem fexs = dim (1.4)(x+2) = lim (1-4) (x + 2 / At a+u) (-1) Atos Xin teal - lim (-u) (atu) a • Mtu)(x-1) y=1 is the honzontal abymplote of fix) xtas dim -