LAC08 UNIT1 MrG 2013.0530

3106 days ago by LAC2013

#1) piecewise f1(x)=x+3 f2(x)=-x-1 f3(x)=x^2-1 f4(x)=sqrt(1-(x-2)^2) f=piecewise([[(-4,-2),f1],[(-2,-1),f2],[(-1,1),f3],[(1,3),f4]]) plot(f,aspect_ratio=1) 
       
#1a) f1(x)=abs(x+3) f2(x)=abs(-x-1) f3(x)=abs(x^2-1) f4(x)=abs(sqrt(1-(x-2)^2)) f=piecewise([[(-4,-2),f1],[(-2,-1),f2],[(-1,1),f3],[(1,3),f4]]) plot(f,aspect_ratio=1) 
       
#1b) f1(x)=x+3 f2(x)=-x-1 f3(x)=x^2-1 f4(x)=sqrt(1-(x-2)^2) f=piecewise([[(-1,0),f3(abs(x))],[(-3,-1),f4(abs(x))],[(0,1),f3],[(1,3),f4]]) plot(f,aspect_ratio=1) 
       
#3) f(x)=x^4-4*x^2 g(x)=x^3-x h(x)=f(x)/g(x) plot(h(x)) 
       
factor(f(x)) 
       
(x - 2)*(x + 2)*x^2
(x - 2)*(x + 2)*x^2
factor(g(x)) 
       
(x - 1)*(x + 1)*x
(x - 1)*(x + 1)*x