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

Question
Answer 1

The end behaviour will be determined by the term of highest degree. In this case we get:

#x^3+3x+2 -> +oo# as #x->+oo#

and

#x^3+3x+2 -> -oo# as #x->-oo#

The end behaviour will be determined by the term of highest degree - in this case #x^3#. Since the coefficient #1# is positive and the degree is odd, we get:

#x^3+3x+2 -> +oo# as #x->+oo#

#x^3+3x+2 -> -oo# as #x->-oo#

If the highest degree was even and the leading coefficient positive we would get #f(x)->+oo# as #x->+-oo#, etc.

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