**Use function notation**

** **

** **When a function *f *is defined with a rule or an equation using *x *and *y *for the independent and dependent variables, we say “*y *is a function of *x*” to emphasize that *y depends on x*. We

use the notation

** y **=

*f***(**

*x***)**,

called **function notation, **to express this and read *f *(*x*) as “*f *of *x*.” (In this special notation the parentheses do not indicate multiplication.) The letter *f *stands for *function*. For example, if ** y **= 9

*x*– 5

*,*we can name this function

*f*and write

*f ***(***x***) **= 9*x – * 5.

Note that *f ***(***x***) **** is just another name for the dependent variable y. **For example, if

*y*=

*f*(

*x*) = 9

*x*– 5 and

*x*= 2, then we find

*y*, or

*f*(2), by replacing

*x*with 2.

*y * = *f *(**2**) = 9 . **2 **– 5

= 18 – 5

= **13**.

For function *f*, the statement “if *x *= **2**, then *y *= **13**” is represented by the ordered pair (**2**, **13**) and is abbreviated with function notation as

*f *(**2**) = **13**.

Read *f *(2) as “*f *of 2” or “*f *at 2.” Also,