How do you find the end behavior of #f(x)= -x^4+x^2#?

1 Answer
Bill K.
Jul 8, 2015

#f(x)->-\infty# as #x->\pm \infty#

Explanation:

The function #f(x)=-x^4+x^2# is a polynomial with a degree of 4 (the largest exponent), which is even. Also, the coefficient of the highest powered term is negative.

These facts are enough to conclude that #f(x)->-\infty# as #x->\pm \infty#. This means that the graph of #f# goes down forever and ever without bound as #|x|# gets larger and larger without bound. To be a bit more precise, the graph of #f# will go below and stay below any given horizontal line by choosing #x# to be sufficiently far from zero.

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