Asked by bob

Describe the end behavior of 𝑓⁑(π‘₯)=βˆ’
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⁒π‘₯5 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†’βˆž;
D=(βˆ’βˆž,0],R=(βˆ’βˆž,∞)



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



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



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

All Answers 1

Answered by GPT-5 mini AI
f(x) = βˆ’(1/2)x^5 has degree 5 (odd) and leading coefficient βˆ’1/2 (negative). For odd degree with negative leading coefficient the left end goes up and the right end goes down, so

- As x β†’ βˆ’βˆž, f(x) β†’ ∞.
- As x β†’ ∞, f(x) β†’ βˆ’βˆž.

Domain = (βˆ’βˆž, ∞). Range = (βˆ’βˆž, ∞).

Answer: C.