The figure shows the graph of the polynomial function y = f(x). For
which of the values k = 0, 1, 2, or 3 will the equation f(x) = k have
complex roots?
The choices are 0, 1, 2, or 3
I'd say k = 3
then we would have:
$\displaystyle f(x) = 3$
$\displaystyle \Rightarrow f(x) - 3 = 0$
However, the graph of $\displaystyle f(x) - 3$ will cut the $\displaystyle x$-axis at in one place. Since it is a cubic polynomial, we should get 3 roots, since we would have only 1 real root if we shift the graph 3 units down, the other two roots will be complex
EDIT: Beaten yet again!