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Question

Identify the right hand and left hand behavior of the graph of the the polynomial function 

 

f(x)= (3-x)^4+2

h(x)=2/7x^3-4x^2-10x+2

k(x)=ax^2+bx+c for a<0 

h(x)= -x

g(x)= 3x^5-6x^3-50

 

Answer 1

f(x) is a 4th degree polynomial & coefficient of leading term will be positive.

g(x) is a cubic with a positive leading coefficient.   Note that I have corrected this function's name, for uniqueness.

k(s) is a quadratic with negative leading coefficient.

h(x) is a well known straight line (odd degree) passing through the origin and having a negative slope

j(x) is a quintic with positive leading coefficient.    Note that I have corrected this function's name, for uniqueness.

 

FUNCTION   BEHAVIOR @ FAR LEFT   BEHAVIOR @ FAR RIGHT   Why?

f                  rises (toward + infinity)   rises (toward + infinity)      even degree, both end behaviors same

g                 falls                                   rises                                     odd degree, 3

k                 falls                                   falls                                      even degree; upside-down parabola

h                 rises                                  falls                                       odd degree, 1

j                  falls                                   rises                                     odd degree, 5