To determine the end behavior of the graph of a polynomial function, we need to analyze the leading coefficient and the degree of the polynomial.

In the given polynomial function of degree three f(x) = 2x^3 – 26x – 24, the leading coefficient is 2 and the degree is 3.

If the leading coefficient is positive, then the end behavior of the cubic graph will be: as x approaches negative infinity, f(x) will approach negative infinity and as x approaches positive infinity, f(x) will approach positive infinity.

Therefore, in this case, the end behavior of the graph of the polynomial cubic function f(x) = 2x^3 – 26x – 24 is: as x approaches negative infinity, f(x) will approach negative infinity and as x approaches positive infinity, f(x) will approach positive infinity.