Question

Which of the functions below could have created this graph?

A. F(x)=x-2x
B. F(x)=x²+5
C. F(x)=-1¹-x²+x+2
D. F(x)=x³+x²+x+1

Answer 1

C. F(x) = -1/2x⁴ -x² +x +2

Explanation:

You want to know which of the offered functions could have created the graph shown.

Leading coefficient

The fact that the graph opens downward means the function has a negative leading coefficient. There is only one such answer choice:

`\boxed{F(x) = -(1)/(2)x^4-x^2+x+2}\qquad\text{Choice C}`

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Additional comment

Both ends of the graph tend in the same direction, indicating the degree is even. (Only even-degree polynomials graph with an "opening direction".)

The offered equation does not actually produce the graph shown. (See attachment.)