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

1 Answer
Aug 21, 2015

Answer:

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#.

Explanation:

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#.