How do you find the end behavior of #f(x) = x^6 + 2#?

1 Answer
Jul 5, 2015

Answer:

Observe that the highest order term is #x^6#. This will be the dominant term for large values of #x#. Since its coefficient is positive and its degree is even #f(x)->+oo# as #x->+-oo#

Explanation:

For polynomials, the end behaviour is dictated by the highest order term.

If the coefficient of the highest order term is positive and the degree is even then #f(x)->+oo# as #x->+-oo#.

If the coefficient of the highest order term is positive and the degree is odd then #f(x)->+oo# as #x->+oo# and #f(x)->-oo# as #x->-oo#.