Question

Please Show ALL Work

111. Use the guidelines to sketch the curve. 1. Find the domain 11. Find Intercepts Symmetry (Even or Odd Function) iv. Asymptotes V. Increasing/Decreasing Intervals vi. Local Extrema Concavity and Inflection Points viii. Sketch the Graph with all above information vii. b) y = 15-5%

Answer 1

b) y=x2-3x i. Find the domain 11. Find Intercepts 111 iv. Asymptotes v. Slace, Y=f(x) is defined for all real values of X, therefore domain is (-00,00). For x-Postercepts, selling x=0, we get xx45)=0 *(x²85) (x²+55)=0 x(x~5"A) (x+54) (x²+15)=0 > x=0,5/4, -514 are x-Portercefits. y-intercepts plug-in x=0 to get y=0 Symmetry (Even or Odd Function) Here we have f(-x) = (-x)?-51-x) = -x75x=-(45-5x) 6---f(x) So, function is odd function & the Snaph is symmetric about y-axis, Graph is a simple sodymamsal and has NO as yomptates. Increasing/Decreasing Intervals we have dy dx = 5x45 - dy/dx=0 at x = 11, Since, dy dx >0 for Ixl> 1 Increasing internals (oo,-1) & (1,00) & dy/dxco for 1x]<1 > Decreasing internal is (4,1). We have, d/d x2 = 20x² and so for X=-), local maxiona d2/1x2 > 0 for x=1 » Local minimum point. So, (4,4) is local maxiora & C1,-4) is local minions points. dzy/dx² =0 for x=0 Point of inflection at cool Concavity and Inflection Points (-1.4) we have, dry/dx2 = 20x² which is to for x> Concare up and co for xco emcevedown Porost of inflection (0,0) C-a, o) Sketch the Graph with all above intormauon figure: Graphis shown for (-1.495, 0) (1.495, 0) zelenors have V1. Local Extrema vu. O,00 viii. -2 0 2 (1, -4)