The leading coefficient is the coefficient of the term with 
the largest exponent of x. That term is x9 and its
coefficient is 1 understood.

The degree IS that largest exponent 9 

That degree is odd, because 9 is odd.

RHEB (right hand extreme behavior) is upward because the leading
coefficient 1 is POSITIVE.

LHEB (left hand extreme behavior) is downward because the rule is:

     1.  If the degree is even, the LHEB is the SAME as the RHEB
     2.  If the degree is odd, the LHEB is OPPOSITE the RHEB  

     and since the degree 9 is odd, it is opposite the RHEB. 
    
The domain of every polynomial function, EVEN or ODD, is (-∞,∞)

The range of every ODD-DEGREE polynomial function is (-∞,∞)

[However the range of an EVEN-DEGREE polynomial is NEVER (-∞,∞),
but is always either (-∞,MAXIMUM], or [MINIMUM,∞), where
the maximum or minimum is a finite real number]

But this one is an ODD polynomial, so its domain and its
range are both  (-∞,∞)

Here is its graph



Edwin