Question

Which polynomial function could be represented by the graph below?

Answer 1

Answer:

third answer

Step-by-step explanation:

The end behavior of the function indicates that the leading coefficient of x is negative (as x approaches infinity, f(x) approaches negative infinity for cubic functions with negative leading coefficients). This eliminates the first 2 answers. Next, factor out the common factor from the 3rd answer and set it to 0 to see if the roots of the polynomial shown on the graph (x=-3, x=2) match that of the answer.

• factor out -2x since each term in the 3rd answer is divisible by -2x => -2x(x^2+x-6)

• set the factored polynomial equal to 0 => -2x(x^2+x-6)
• divide both sides by -2x => 0 = x^2+x-6
• factor => (x+3)(x-2) = 0
• find zeros by setting both factors equal to 0 => x=-3, x=2

This means that the 3rd answer is correct. The last answer, while having the correct leading coefficient, will produce roots of 3 and -2 instead of -3 and 2, which is shown on the graph.