The discussion centers on the graphing of the function y = (-2)^x, which is deemed "impossible" to graph due to the presence of imaginary numbers for non-integer values of x. While integer values yield real numbers that can be plotted, fractional exponents lead to square roots of negative numbers, resulting in undefined or imaginary outputs. Participants clarify that y = -2^x and y = (-2)^x are distinct functions, with the former being a reflection of y = 2^x across the x-axis. The significance of the even denominator in rational numbers is highlighted, as it leads to complications when attempting to take roots of negative numbers. Overall, the inability to graph y = (-2)^x arises from the limitations of real number outputs for certain values of x.
