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How do you find the end behavior of #-x^3+3x^2+x-3#?

Answer 1

Madelyn Anderson

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

#"consider the term of highest degree"#

#-x^3" is of odd degree and has a negative coefficient"#

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

#rArrlim_(xto-oo)f(x)to+oo# graph{-x^3+3x^2+x-3 [-10, 10, -5, 5]}

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Answer 2

Christian Antunez

To find the end behavior of the polynomial -x^3 + 3x^2 + x - 3:

Examine the leading term: The leading term is -x^3. Since the degree of the polynomial is odd and the coefficient of the leading term is negative, the end behavior will be as follows:
- As x approaches negative infinity, the function will decrease without bound (tend to negative infinity).
- As x approaches positive infinity, the function will increase without bound (tend to positive infinity).

So, the end behavior of the polynomial -x^3 + 3x^2 + x - 3 is:

As x approaches negative infinity, the function decreases without bound.
As x approaches positive infinity, the function increases without bound.

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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.