#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)
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#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)
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#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)
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#3)
f(x)=x^4-4*x^2
g(x)=x^3-x
h(x)=f(x)/g(x)
plot(h(x))
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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 |
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