f(x)= -1/4x^6 +4x^4 -x^3 +7

Hello

With a negative leading coefficient?

Graph:

so what would the end behavior be?

wait wouldnt it be reflected over the x since theres a negative?

That is what the end behavior would be called for the given function (Answer is: "with a negative leading coefficient"). Can also read more here on this topic:

http://www.purplemath.com/modules/polyends.htm

Basically you're checking if the right hand side of the graph signals a positive or negative function.

To your second question you can still write it as (-1/4) x^6 due to the order of division and multiplication

i thought the end behavior had to have infinity in it

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