These are vertical transformations or translations, and affect the \(y\) part of the function. When functions are transformed on the outside of the \(f(x)\) part, you move the function up and down and do the “ regular” math, as we’ll see in the examples below. When looking at the equation of the moving function, however, we have to be careful. There’s also a Least Integer Function, indicated by \(y=\left\lceil x \right\rceil \), which returns the least integer greater than or equal to a number (think of rounding up to an integer).Īgain, the “parent functions” assume that we have the simplest form of the function in other words, the function either goes through the origin \(\left( \right)\) *The Greatest Integer Function, sometimes called the Step Function, returns the greatest integer less than or equal to a number (think of rounding down to an integer). Just like our own families have parents, families of functions also have a parent function. In mathematics, we have certain groups of functions that are called families of functions.
Well, that’s not exactly right however, there are some similarities that we can observe between our own parents and parent functions. All quadratic functions have the highest exponent of 2, their graphs are all parabolas so they have the same shape, and they all share certain characteristics. The similarities don’t end there! In the same way that we share similar characteristics, genes, and behaviors with our own family, families of functions share similar algebraic properties, have similar graphs, and tend to behave alike.Īn example of a family of functions is the quadratic functions. Parent Functions: When you hear the term parent function, you may be inclined to think of two functions who love each other very much creating a new function.
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