A parameterized function can be represented in two equivalent ways. The general form, $o = g(x_0, x_1, \dots, x_m; \theta)$, explicitly lists the parameters $\theta$ after the input variables. A more concise shorthand notation, $g_\theta(x_0, x_1, \dots, x_m)$, moves the parameters to a subscript of the function name. The equivalence is expressed by the equation: $o = g(x_0, x_1, \dots, x_m; \theta) = g_\theta(x_0, x_1, \dots, x_m)$. This subscript notation emphasizes that the function's behavior is determined by the parameter set $\theta$.