Functions and Critical Values Test Corrections

6)  Given the function y=20x^7-10x^3/5x^3
a) State the end behavior of the function and explain how you can determine the end behavior without graphing the function.
What I had:
end behavior: as x approaches infinity f(x) approaches infinity
as x approaches negative infinity f(x) approaches negative infinity
If the greatest exponent is odd and the leading coefficient is positive, the above will be the end behavior.
Why this is wrong:
I did not simplify the function.
Simplified, the function is 4x^4-2.
The right answer:
end behavior: as x approaches infinity f(x) approaches infinity
as x approaches negative infinity f(x) approaches infinity
If the greatest exponent is even and the leading coefficient is positive, the above will be the end behavior.

b) State the intervals where the function is increasing and decreasing.
What I had: increasing for all real numbers
Why this is wrong: I put the equation into the calculator without parentheses around the numerator and denominator.
The right answer: decreasing {x/0>x} increasing {x/0<x}

This unit was fine as it was pretty much a review from last year, but I didn't ever memorize the end behavior rules.