Question

Describe the end behavior of a 14th degree polynomial with a positive leading coefficient.

Answer 1

The function will enter the graph graph in the upper left hand region and exit in the upper right hand region and overall the graph will be concave upwards.  
For determining the end behavior of a polynomial, there is just 2 things to take notice of. 
1. Is the leading coefficient positive or negative? 
2. Is the degree of the polynomial odd or even?  
For odd ordered polynomials, the curve starts in either quadrant II or III, and ends in quadrant IV, or I. Basically, if it's positive, the curve enters the graph somewhere in the lower left hand region, and exits the graph in the upper right hand region. If the coefficient is negative, it enters in the upper left hand region, and exits in the lower right hand region.  
For even ordered polynomials, the graph is either concave upwards (positive leading coefficient) or concave downwards (negative leading coefficient).  
In this problem, 14 is an even number and since the coefficient is positive, the function will enter the graph graph in the upper left hand region and exit in the upper right hand region and overall the graph will be concave upwards.