Here are the rules for determining end behavior on all 
polynomial functions:  

Find the leading term, which is the term with the 
largest exponent.

1. Is the leading term's coefficient positive? Then it goes 
up one the right end.

2. Is the leading terms' coefficient negative? Then it goes 
down on the right end.

3. Is the leading terms' exponent even?  Then it goes the same 
way on the left end as it does on the right end.

4. Is the leading terms' exponent odd?  Then it goes the 
opposite way on the left end than it does on the right end.    


Let's go thru those rules with your polynomial


    
Find the leading term, which is the term with the 
largest exponent.

That's 

1. Is the leading term's coefficient positive? 

No, it's -2 and that is negative.

2. Is the leading terms' coefficient negative? 

Yes, for -2 is negative.

Then it goes down on the right end.

3. Is the leading terms' exponent even? 

No, it's 3 which is odd.

4. Is the leading terms' exponent odd?  

Yes, for 3 is odd.

Then it goes the opposite way on the left end than 
it does on the right end.    

Since it goes down on the right, it goes up on the left
end.

In a nutshell, the rules are: 

1. positive coefficient, up on right end.
2. negative coefficient, down on right end.
3. even power, left end same as right end.
4. odd power, left end opposite from right end.


Edwin