One simple kind of transformation involves shifting the entire graph of a function up, down, right, or left. The simplest shift is a vertical shift, moving the graph up or down, because this transformation involves adding a positive or negative constant to the function. In other words, we add the same constant to the output value of the function regardless of the input. For a function \displaystyle g\left(x\right)=f\left(x\right)+kg(x)=f(x)+k, the function \displaystyle f\left(x\right)f(x) is shifted vertically \displaystyle kk units.
