Function Notation

**Function Notation**

When a function is expressed as an equation, it is often written as "*f*(*x*)." In creating a table of values for an equation, for example *y* = 5*x* - 1, we use this rule, "multiply by five and subtract one" to transform an input *x* value into the one resulting *y* value. By giving the expression "multiply by five and subtract one" the name *f*, we have an easy way to show that we're applying the rule to different numbers and variables.

In general, the symbol *f*(*x*) replaces *y* and is read as *f* of *x*, which does not mean *f* times *x*. It means the value of expression *f* for a given value of *x*.

**Example**

Evaluate the function for the given value of the variable.

*f*(*x*) = 5*x* - 1 when *x* = 3

**Graphing a Linear Function**

Since the function notation lets us write *f*(*x*) instead of *y*, the graph of a function *f* is the set of all points (*x*, *f*(*x*)), where *x* is in the domain of the function.

**Example**

Graph *f*(*x*) = 5*x* - 1 and find the value of *f*(3) by using the graph.

The *y*-intercept is -1 and the slope is 5. When *x* = 3, *y* equals 14. This confirms the answer found in the previous example.