Question

use the leading coefficient test to determine the end behavior of the graph of the given polynomial function f(x)=3xexponent7 - 7xexponent6 + 3x exponent 5 + 5

Answer 1

So you have:
\[f(x)=3x^7-7x^6+3x^5+5\]
I'm not exactly sure what the leading coefficient test is. But it is an odd power So it has one end going up (+infinity) the other going down (-infinity). Then the 3 is POSITIVE. So it should be up when x gets arbitrarily large and down when x gets arbitrarily small.
Which it does: http://www.wolframalpha.com/input/?i=plot+f(x)%3D3x^7-7x^6%2B3x^5%2B5