Final answer:
The end behavior of the graph of q(x) is that as x approaches positive or negative infinity, the graph will rise on both sides.
Step-by-step explanation:
The end behavior of a polynomial function is determined by the degree and leading coefficient of the polynomial. In this case, the polynomial function is q(x) = 3x4 - 5x3 - 2x2 + x - 18.
The degree of the polynomial is 4, which means that as x approaches positive or negative infinity, the graph of q(x) will have a similar behavior to that of an even-powered function, where the arms of the graph point up. Additionally, the leading coefficient is positive (3), which means that the arms of the graph will both point upward.
Therefore, the end behavior of the graph of q(x) is that as x approaches positive or negative infinity, the graph will rise on both sides.