Transformations of parent functions involve the movement of a basic algebraic function away from its original location. Because most parent functions pass through the origin (0,0) in the Cartesian coordinate system, transformations of these functions may result in a graph that looks similar to the parent function but does not intersect the origin.
Parent function transformations may be done as shifts, either vertically or horizontally. Vertical transformations involve a shifting of y-coordinates either up or down. An example of a vertical transformation is the shifting of an algebraic function two units up. This results to a slight change in the algebraic function from y to y + 2, which signifies the upward shift. Similarly, a horizontal transformation is the shifting of a graph to the left or to the right. When this happens, the value of x is either added to or reduced by the number of units that the graph shifts. For instance, if a function is moved three units to the left, then the original x value becomes x - 3. In many cases, transformations of parent functions involve a combination of vertical and horizontal shifts.
Another type of parent function transformation involve changes in magnitude, which result in either shrinking or expanding the graphical depiction of the function. In algebraic terms, this is achieved through multiplication or division. Any algebraic function may be traced back to its parent function using the concepts of shifts and magnitude.