Question

y = ģ ( - 32+2) -. (2 f(3) = xen 5 i fix) 2 5x

Answer 1

Solution U Da y = (re?-32+2) 3 C-00,00) Domain the of gives function is then Now put y=0 find intercepts - cs put x=0 y = 2 then y intercept is jisi we get (x²-3x+2) =0 (2-10(x-2)=0 K=1,2 X Invercepts que (2,09 and 41,0) we have (x2-3x+2) then Now which is in the a e²+bx+c form of (Equation of parabola) on comparing y = 1: 2 - x + 2/2 we get a 1 c=2 a=1/3 b=-1 > 3 the neuter parabola an up-down facing of of the form of Xv= -6 aa Ki= -(-1) ello 2.13 and y v = 1 -L 12 the veutex Parabola is therefore 12 if a so then vertex is Minimum value. then veutex is a Maximum value of Here, it aco

- M Range of 22-32+2 veutere. (xw, yu) it a so the range is f(2)= qu if a co range is f(x) = you the f(x) = -1 then the Range is Tit,co); Hence, X Intercepts que e intercept 14 (2,0), and CIO) is and Ger 72 4 is x=2. 3 Axis of symmetry Extreme points Minimum ( t) Asymptates 12 None vingtection Points - None

fc2l= I ker Domain of fire)= + ker 15 '10 0 54 2 2 -10 F-15 Houe 201 ou x>0 Domain of f(x) = (-0,0) 1 (0,00) critical point = f'(x)=0 -0 . ltr ex 1 x=-1 -0022-1 then -1<x<0 02220 internal Monorone the function -12X40 OLX 200 <X20 -02X-1 0 + sig? Behaviour incuea Xem into f Now easing Maximum Decreasing Decreasing plung y = here eget, [y=-e Maximum (-1,-1) we . !!

Asymprotes of y = f(x) = 1 here veutical Asymptotes of f(x) zez xex_o X=0 Houizontal Asymprotes of fire) 4=0 Symmetry of f(x) = None inflection points of f(x)=None. there is no intercepts points. o and Range of free ferreme point -(Maximum (-4,-2)).' 2 then f(2)s-e -f62) {-en ou f(2)>0. for -00<x<0 Orco and of f(x) 200 for Hence, is I aer Range of f(x) ---23060)

3) (-00,00) cij =0. f(x)= x5_52 Is Domain of function find intercept points dif x=0 y=0 (0,0) if you 25-5x=0 x(ne"-5)=0 +415. and. x=0 4 x= thes 9 y inercept X intercepts points que (0,0) (-45,0) and C 415,0) point is (0,0) cuitical points plcx)=0 574_5=0 8241 x=+1 function Monrone intervals are. then, the -LX-1 ,-KX<!,, 1<x<0 internal OLXZ-1 X=-11 -1<x< X=1 12x20 sign 0 + Behavior increa easing Maximum Decreasing minimum ince increasing put X=-1 into 25_52 → f(x)=4 then x= unro 25_52 Maximum (-1,4) and & f(x)=-4 then Minimum (1,-4) Range of f(x)= (-00,00) Asymprotes - f(x) = None of

6 4 inflection points f(x)=75-6% plcx)= 524-5 f'(x)= 20C3 inflection points are in Domain edges, gon8=o Heue mot on x=0 y=0 LOCK > OCXL interval -00 2x20 2=0 022 200 + sign Behaviour concave Doonwald unglection concave to lepward ny 5 -5 >n ust -5 Guiaph is Symmetric about origin. Solved