Which graph represents the function?
2 answers:
Of course, I would just graph it on Desmos.com or my graphing calculator and be done.
f(x) can be factored as
.. f(x) = (x -6)(x +1)/((x -3)(x +2))
so will have zeros at x = {-1, 6}, vertical asymptotes at x = {-2, 3}, and sign changes at all of those points.
The Upper Right graph is the only one with the zeros and asymptotes in the right places.
f(x) can be factored as
.. f(x) = (x -6)(x +1)/((x -3)(x +2))
so will have zeros at x = {-1, 6}, vertical asymptotes at x = {-2, 3}, and sign changes at all of those points.
The Upper Right graph is the only one with the zeros and asymptotes in the right places.
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Descartes' rule of signs tells you the one sign change in the coefficients means there's one positive real root. If you change the sign of the odd-power terms, the signs become -++-, so have two sign changes. This means there are 0 or 2 negative real roots.
A graph shows there to be 3 real roots, two of which are negative. Thus there are no complex roots.
A graph shows there to be 3 real roots, two of which are negative. Thus there are no complex roots.