Question

Which of the following could represent the graph of f(x) = y3 – x2 - 6x?

Answer 1

Answer: A

Step-by-step explanation:

$x^{3}-x^{2}-6x=0 \\ \\ x(x^{2}-x-6)=0 \\ \\ x(x-3)(x+2)=0 \\ \\ x=-2, 0, 3$

So there needs to be roots at x=-2, 0, and 3.

Also, the end behavior needs to approach infinity as x approaches infinity and negative infinity as x approaches negative infinity (since the leading coefficient is positive). This rules out the last option.

Now, we can also use the fact that the maximum number of turning points is one less than the degree, for a maximum of 2 turning points. This rules out the middle option as well.