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What is the end behavior of the function #f(x)=x^2+x^4+6#?

Answer 1

Serenity Johnson

#lim_(xto+oo)f(x)to+oo#

#lim_(xto-oo)f(x)to+oo#

#"the term with highest degree in f(x) is "x^4#

#"the degree is even and has a positive coefficient"#

#rArrlim_(xto+oo)to+oo#

#lim_(xto-oo)to+oo# graph{x^2+x^4+6 [-40, 40, -20, 20]}

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Answer 2

Sadie Ackerman

The end behavior of the function f(x) = x^2 + x^4 + 6 is that as x approaches positive or negative infinity, the function increases without bound. This is because the leading term, x^4, dominates the behavior of the function as x becomes large, causing the function to approach positive infinity.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.