## Algebra## Algebra Explained |

## What are functions? |

Functions are mathematical expressions describing the relationship between variables and involve only algebraic operations. If there is one independent variable, the dependent variable, for example *y,* can be determined through the function. This is often seen written as *y* = *f*(*x*), spoken as, “y equals fof x” (functions also use notation with *x*; for example, *f*(*x*) = 2*x* + 1 is a function). Functions within equations are also common; for example, in the equation -*x*^{2} + *y* = 3, the *y* represents a function of *x*. To see this, note that this equation can also be written as *y* = 3 + *x*^{2}.

Functions do not always have to be in terms of *f(x)*. They can just as easily be termed *g(x)*, depending on the equation. But note: The equation *x*^{2} + *y*^{2} = 9 is *not* a function, as *x* and *y*are both independent variables.