Question

For the function f(x) = -**-4x find the following, and use it to graph the function. Find: a) (2pts) Domain b)(2pts) Intercepts c)(2pts) Symmetry d) (2pts) Asymptotes e) 4pts) Intervals of Increase or decrease f) (2pts) Local maximum and local minimum values g)(4pts) Concavity and Points of inflection and h)(2pts) Sketch the curve

Answer 1

of_ar ald fla) = 012-404 3012 – 1001-0 to Donain of f(a)= 3o7-187-8 Take the denomina for(s) of the compare to zero 337-187-8=0 3012-1204+201-8=0 » 30(7-4)+2671-2)=0 (391+2)(01-4) = 0 01 = = = 4 1. OK-25 or 2 <* <4 or 0742 I interval Notation (-0,27%) u (22 3 , 4) u (4,0) = I key point. The domain of a tunition is the st of input or argument values for which the function is read any defined.

E - interupt of f(x) = f(2)= of 4th 302-107-8 2 - where y=0 012-486 to 3012 104-8 : 220 E E got poist (0,0) g- axis interpept point in the gooph whire x=0 24.0 y = ²4.0 gro 3.02-10.0-0 2. Cool X - interceptas: (0,0) ..y istercept: (0,0)

x240 © Symmetry of f(2)= 30%-107-8 denominator to 3012-1001 - 870 937-1994+201-8 to * 37(7-4) +2(3-4) to » (0i-4) (32+2) to » 274, 27-2 i t -6 ż to 1 6 -4 2 ttt

② Asymptotes of f(2)= 7245 87²-187-8 +(91) = 32 401 f(1) = 322107-8 n(21-4) (01-45 (30172) 0 8072 f(1) = For rational furition, the vestical asymptote are the undefined polito, also known as the zoos of the denominator of the simplified fonetin 30+2=0 -? The vertical assymptotes - 27 Note For Hosszesful asymptotes for of national - it denominator's degree > hymerator's degree the Lorizontal approptotes is the x-axip, y=c if nymerator degree =lt derminator is egree, the

The asymptotep is a slast asymptotes of from: y = moctb if the degree are equal, the gas pompotes is g= hymerater leading coeffined denominator's leading coefficist f(2)= a Nymerafor 's leading coefficist = 1 derminator's leading coeffinnst =3 - 30172 is/ The Asizestal asymptotes • Interval of increase or decrease - 2401 307_10010 f'(a)= a[ n(0-4) dal (3842) (81-4) f'() = m ( 30tz]

1191)=(337-1001-e)[201 – 4) - [667 -19)(012471)] .. (302100-oj 2 fl( on +(60123–2007_169-1207740381 +24) - [633_1007-246750m - (387-you-o2 1 682_3207242441 +24-67463 +3402-4001 . (30²197492 282_168724 f(n) = (332 -10m+@j2 point 0 = 287-167724 .e for critical (322-187+82 . f(2)=0 OF 2(712881712) » 0²-82+12=0 7 82-67-28+12=0 → 31001-0)-2689-6)=0 ☆ (81-6)(01-2) =0 + (2) = 282102724 1 2 6 (30²-10779 increasing (-0, 2]u[6,0) deereasing [2,6

t o for loof maxing and local minina - (81)= 240 381-1990 +(61) = 222_161124 (3072-108-02 at stationery point f'(x)=0 2872 1687+24 -0 * x2 811+12=0 - 01=2,6 7(01) = (8-4) (21-4) (3072) 3072 f'(21) = (33142) 32 = x (331722 (35+23 2 X f"(n)= -2X2X3 (37+233 -12 b = - = -0.0234 128 f'(2) -0.0013 fy(6) Jo )