How do you describe the end behavior of #f(x)=x^2-8x+18#?

1 Answer
Sep 29, 2016

Answer:

as #xrarr-oo, f(x)rarr+oo# and
as #xrarr+oo, f(x)rarr+oo#

Explanation:

#f(x)=color(red)1x^color(blue)2-8x+18#

Because the degree #color(blue)2# is even, this an even function. Even functions have end behaviors that both go in the same direction in y.

The function has a positive leading coefficient, #color(red)1#. Even functions with positive leading coefficients have end behaviors that both go toward positive infinity (both ends of this quadratic/parabola graph point "up").

In other words,

as #xrarr-oo, f(x)rarr+oo# and
as #xrarr+oo, f(x)rarr+oo#