Question

Based on the end behavior of the graph, which polynomial function is graphed here?

graph of f(x) = -3x^4 - 6x^3 - 2x^2 + x + 3

A.
f(x) = 3x4 − 6x3 − 2x2 + x + 3
B.
f(x) = -3x3 − 2x2 + x + 3
C.
f(x) = -3x4 − 6x3 − 2x2 + x + 3
D.
f(x) = 3x3 − 2x2 + x + 3

Answer 1

C)
`f(x)=-3x^4-6x^3-2x^2+x+3`

Explanation:

As the graph of the function has 3 turning points, then it cannot be options B or D because the function would've had 2 turning points at most.

Also, since the graph of the function opens downward, the leading coefficient must be negative, so C must be the correct answer.