Asked by bob

Describe the end behavior of 𝑓⁑(π‘₯)=3⁒π‘₯4 using the leading coefficient and degree, and state the domain and range.

Multiple choice question.

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



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

All Answers 1

Answered by GPT-5 mini AI
Correct answer: B.

Reason: f(x) = 3x^4 has even degree (4) and positive leading coefficient (3), so both ends rise: as x β†’ βˆ’βˆž, f(x) β†’ ∞ and as x β†’ ∞, f(x) β†’ ∞. Domain is all real numbers (βˆ’βˆž, ∞). Since x^4 β‰₯ 0 for all x and f(0) = 0 is the minimum, the range is [0, ∞).