Question

i need help with c, d, and e

3. Use the following steps to sketch the graph of each of the following functions. Step 1: Find the domain. Step 2: Find the y-intercept and all x-intercepts. Step 3: Decide if the function has any symmetry: odd, even, periodic. Step 4: Find any horizontal or vertical asymptotes. Justify using limits. Step 5: Find the critical numbers and determine intervals of increase/decrease. Step 6: Identify all local extrema. State as ordered pairs. Step 7: Determine intervals of concavity and identify any inflection points (as ordered pairs). Step 8: Use the information gathered in Steps 1 through 7 to sketch an accurate graph. a. y = (4 – x2)5 b. y = Vx2 + x - x c. y = x + cos x d. y = tan-?(e*) e. y = ln(1 + x3)

Answer 1

$6) = f(-x) = Even function - By the 'Holizontal Assymptote name Lim (4-22)5 - O Portable prezi No Horizontal Assym plote Vertical Assymptote As, for ud any pcorticulos Value of x, this is not defined some → No Vertical Assymptoto ale; lim (4.2%) 5 + 6 Vertical 1- 4' 15 (42-X)*(-22) --[X-0 (4-x)+ 0 7 2 +2

Ans: @) y(4-x white 1. → Domain = (-0.01) abril y Intercept where y = (4 x 75 led by people in and x=0 and y= (4) at delen y = 1024w more le; (0,1024) we can say . x- Intercept where y=0, let us know > y=64-205-0 xt time 12 So, that, (-2,0) and (+2,0) By replacing that x by x → 9: (4-(-2)); 6 -20°)5 So, We Can Assume that

that hade 109 So, Points of infection - -2,2 + 2 , 2/3 nunun -2 -2/3 2/2 con care upwbold Concave downward > 62,-23) (23;2) (-2,-2) 0 (-2/3, 2/3) 0(-2. LI - -2 -2/3 o 2/3 2 ar (6) Y Jat2 - → domain (-6, -1]0[o,.). → X- Intercopt (0,) y Intercept coo Hỡi la Aurploa 3 -

So, 0, 23-2, y= 1024, yo Gritical points:- q do - Inteural g Increase → (D), -2) 0(-2,0) ontowal of decrease = (0,2) 062,-0) to local la (116)= (0,102 is local Maxima y"=-10 Canon (4-)4+ (4 -10€ do). E-10 (, 4cu-x (-20) + (4-2014] 9"= + 80X(4-»*) 3–10 (4-)4 9" (4- 3 180x9-10(4-20] -0. (4-22):20 Sox 40 +020-0 4-X=0 102-40=0 X: 2 2 = 40/90 5 x = +23]

Hon Vertical Assymptote Critical points Y? - (2x +1) - 50 2data = x= -1,0 Not in domain Ontwaal of Increas -7 COB) wteval o decrear + (0, -1) to Local Minima No local aume g . 46161713272 H6 Inflection points. plotting the graph: