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How to Graph Polynomial Functions Using Transformations

Function transformations refer to operations that have been performed on a function that changes its graph. These operations allow for graphs of simple functions to be created without the need to plot numerous points. Instead, the graph of the primitive function is placed on the coordinate plane and then moved, or transformed, into a new position. This topic is first encountered in intermediate algebra and finds uses in calculus as well for graphing with derivatives.

Instructions

- 1
  Graph the base function within the functions that have been transformed. For example, in the function f (x) = (x^2) + 2, x^2 is the base function.
- 2
  Move the graph to the up or down on the x-axis based on any additions or subtractions present beside the base function. If the term added to the base function is positive, the function is moved up the y-axis. If the term added is negative, the function is moved down the y-axis.
- 3
  Move the graph left or right to compensate for any changes made "within" the function. For example, the function f (x) = (x - 2)^2 has a subtraction within the squaring function. If this additional term is negative the function is moved to the right. If the value is positive, the function is moved to the left.
- 4
  Flip the graph about the x-axis if the function has a negative sign outside of it. For example, the function (-f (x) = x^2) should be flipped about the x-axis.
- 5
  Flip the function about the y-axis if there is a negative sign within the function. For example, f (x) = (-x^2) should be flipped around the y-axis.

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