Asked by bob

Describe the end behavior of 𝑓⁑(π‘₯)=βˆ’2⁒π‘₯3 using the leading coefficient and degree, and state the domain and range.

Multiple choice question.

A)
As⁒π‘₯β†’βˆ’βˆž,𝑓⁑(π‘₯)β†’βˆžandas⁒π‘₯β†’βˆž,and⁒𝑓⁑(π‘₯)β†’βˆ’βˆž;
D=(βˆ’βˆž,∞),R=[0,∞)



B)
As⁒π‘₯β†’βˆ’βˆž,𝑓⁑(π‘₯)β†’βˆžandas⁒π‘₯β†’βˆž,and⁒𝑓⁑(π‘₯)β†’βˆž;
D=(βˆ’βˆž,0],R=(βˆ’βˆž,∞)



C)
As⁒π‘₯ β†’βˆ’βˆž, 𝑓⁑(π‘₯) β†’βˆž and as⁒π‘₯ β†’βˆž, and⁒𝑓⁑(π‘₯) β†’βˆž;D =(βˆ’βˆž,0), R =[0,∞)


D)
As⁒π‘₯β†’βˆ’βˆž,𝑓⁑(π‘₯)β†’βˆžandas⁒π‘₯β†’βˆž,and⁒𝑓⁑(π‘₯)β†’βˆ’βˆž;
D=(βˆ’βˆž,∞),R=(βˆ’βˆž,∞)

All Answers 1

Answered by GPT-5 mini AI
f(x) = βˆ’2x^3 is an odd-degree (3) polynomial with negative leading coefficient (βˆ’2). So as x β†’ βˆ’βˆž, f(x) β†’ ∞, and as x β†’ ∞, f(x) β†’ βˆ’βˆž. Domain = (βˆ’βˆž, ∞), Range = (βˆ’βˆž, ∞).

Answer: D.