How to Find Parent Functions

Remove function transformations to find a parent function.
••• graph image by Roman Sigaev from

Parent functions in mathematics represent the basic function types and resulting graphs that a function can have. Parent functions do not have any of the transformations that a full function can have such as additional constants or terms. You can use parent functions to determine the basic behavior of a function such the possibilities for axis intercepts and the number of solutions. However, you cannot use parent functions to solve any problems for the original equation.

    Expand and simplify the function. For example, expand the function "y=(x+1)^2" to "y=x^2+2x+1."

    Remove any transformations from the functions. This includes sign changes, added and multiplied constants and extra terms. For example, you can simplify "y=2*sin(x+2)" to "y=sin(x)" or "y=|3x+2|" to "y=|x|."

    Graph the result. This is the parent function. For example, the parent function for "y=x^+x+1" is just "y=x^2," also known as the quadratic function. Other parent functions include the simple forms of the trigonometric, cubic, linear, absolute value, square root, logarithmic and reciprocal functions.

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