Suppose the polynomial f(x) has the following end behavior: as x→∞, f(x)→−∞, and as x→−∞, f(x)→−∞.

Which of the following polynomials could represent f(x)?

There may be more than one correct answer. Select all correct answers.

a. −x2

b. 2x^4−x^3−x^2−x−1

c. −5x^6+10x^5−3x^2+9

d. x^2

e. −2x^3+16x

Please select ALL answers

  a. −x2

  c. −5x^6+10x^5−3x^2+9

Step-by-step explanation:

The signs of the end values of f(x) are the same, so the polynomial is of even degree. (Eliminates choice E.) The signs are both negative, so the leading coefficient of the polynomial is negative. (Eliminates choices B and D.)

The appropriate choices are ...

  A: 2nd degree with negative leading coefficient

  C: 6th degree with negative leading coefficient