1) Reflections of functions f(x) over the x-axis or y-axis produce new equations by changing the sign of the y-values or x-values respectively. 2) The inverse of a function f(x) is denoted f^-1(x) and is found by switching the x and y values when graphed, effectively reflecting over the line y=x. 3) For example, the inverse of f(x)=2x+5 is found by graphing f^-1(x) which treats x as the output and y as the input.