SOLUTION: (infinity sign) stands for where an infinity sign is supposed to be (_) stands for where an arrow is supposed to be What is the end behavior for the polynomial function f(x)=-6x^

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Question 961006: (infinity sign) stands for where an infinity sign is supposed to be
(_) stands for where an arrow is supposed to be
What is the end behavior for the polynomial function f(x)=-6x^4 +3x^2 -7 ?
a. x(_)-(infinity sign),f(x)(_)(infinity sign)
x(_)(infinity sign),f(x)(_)-(infinity sign)
b. x(_)-(infinity sign),f(x)(_)(infinity sign)
x(_)(infinity sign),f(x)(_)(infinity sign)
c. x(_)-(infinity sign),f(x)(_)-(infinity sign)
x(_)(infinity sign),f(x)(_)-(infinity sign)
d. x(_)(infinity sign),f(x)(_)(infinity sign)
I'm sorry if (_) and (infinity sign) makes the answers difficult to understand.
Answer by MathLover1(20855) About Me  (Show Source):
You can put this solution on YOUR website!
"End behavior" asks what happens to y as x gets arbitrarily large
is a positive and in a negative direction. The highest power term
determines what happens.
As x gets very positively large -6x%5E4 gets very negative so the end behavior is:
as x goes to infinity, y goes to -infinity
As x gets very negatively large -6x%5E4 gets very negative(any negative number to the power of 4 becomes positive) so the end behavior is :
as x goes to -+infinity, y goes to -infinity+
or
lim%28x-%3Einfinity%2C%28-6+x%5E4%2B3+x%5E2-7%29%29+=+-infinity
lim%28x-%3E-infinity%2C+%28-6+x%5E4%2B3+x%5E2-7%29%29+=+-infinity


+graph%28+600%2C+600%2C+-5%2C+5%2C+-55%2C+5%2C+-6x%5E4+%2B3x%5E2+-7%29+