What is the end behavior of the graph of the polynomial function f(x) = 2x3 – 26x – 24?

The end behaviour to the left is decreasing and to the right is increasing

The end behaviour of a polynomial function depends on the degree "n" of the polynomial ("n" even or odd) and the sign on the leading coefficient (the coefficient of the "x" has the biggest exponent):
For even degree polynomial (biggest exponent "n" even) and leading coefficient positive the end behaviour is increasing in both ends; and for leading coefficient negative the end behaviour is decreasing in both ends.
For odd degree polynomial (biggest exponent "n" odd) and leading coefficient positive the end behavior to the left is decreasing and the end behaviour to the right is increasing; for leading coefficient negative, the end behaviour to the left is increasing and the end behaviour to the right is decreasing.

In this case the degree of the polynomial (biggest exponent) is n=3 (odd) and the leading coefficient (the coefficient of the "x" has the biggest exponent) is 2 (positive), then the end behaviour to the left is decreasing and to the right is increasing