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

Question

Sadie Ackerman · Accepted Answer

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# and #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.

Christian Antunez · Answer

undefined To find the end behavior of the polynomial function f(x) = x^3 + 3x + 2, we examine the leading term, which is the term with the highest degree, in this case, x^3.

For polynomials, the end behavior is determined by the leading term. If the leading term is of odd degree and has a positive coefficient, the end behavior will be as follows:
- As x approaches negative infinity, f(x) approaches negative infinity.
- As x approaches positive infinity, f(x) approaches positive infinity.

Therefore, for the function f(x) = x^3 + 3x + 2:
- As x approaches negative infinity, f(x) approaches negative infinity.
- As x approaches positive infinity, f(x) approaches positive infinity.