so i have an assignment were i should find if theres a symmetry, the intercepts, asymptotes and the regions.. this is the curve y^2 = 6x -11x^2 + 6x^3 -x^4..
i am so lost.. and i dont know if i am still on the right track with what i am doing so someone please help me :(
and i have another question. in this curve, y = (x-1)^2 / x(x-4), is there 4 regions? or is it 5? do i need to include the y intercept where (0,0) as a region or not? thanks in advance
i am so lost.. and i dont know if i am still on the right track with what i am doing so someone please help me :(
and i have another question. in this curve, y = (x-1)^2 / x(x-4), is there 4 regions? or is it 5? do i need to include the y intercept where (0,0) as a region or not? thanks in advance
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1st : symmetry about the x axis { trivial } ; x ≥ 0 {y²} ; easy to see the roots are { 0 , 1, 2, 3 } so
the x intercepts are known, and the graph divides the plane into 5 connected regions { because
of the symmetry }..3 closed & bounded and 2 open and unbounded .
2nd : intercept is (1,0) only ; horizontal asymptote is y = 1 ; vertical are x = 0 & 4 ;
not symmetric about the axes ; domain is broken into 3 parts , thus graph divides
the plane into 6 open and unbounded regions { 2 in each part of the domain }
the x intercepts are known, and the graph divides the plane into 5 connected regions { because
of the symmetry }..3 closed & bounded and 2 open and unbounded .
2nd : intercept is (1,0) only ; horizontal asymptote is y = 1 ; vertical are x = 0 & 4 ;
not symmetric about the axes ; domain is broken into 3 parts , thus graph divides
the plane into 6 open and unbounded regions { 2 in each part of the domain }
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it is not x² - 1 = [ x - 1][x+1]
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