What is the end behavior of the function #f(x) = x^3 + 2x^2 + 4x + 5#?

Answer 1

The end behaviour of a polynomial function is determined by the term of highest degree, in this case #x^3#.

Hence #f(x)->+oo# as #x->+oo# and #f(x)->-oo# as #x->-oo#.

For large values of #x#, the term of highest degree will be much larger than the other terms, which can effectively be ignored. Since the coefficient of #x^3# is positive and its degree is odd, the end behaviour is #f(x)->+oo# as #x->+oo# and #f(x)->-oo# as #x->-oo#.

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Answer 2

Anna Allen

The end behavior of the function ( f(x) = x^3 + 2x^2 + 4x + 5 ) is that as ( x ) approaches positive infinity, ( f(x) ) also approaches positive infinity, and as ( x ) approaches negative infinity, ( f(x) ) also approaches negative infinity. This is because the leading term, ( x^3 ), dominates the behavior of the function for large positive and negative values of ( x ).

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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.