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 = 9x – 5, we can name this function f and write
f (x) = 9x – 5.
Note that f (x) is just another name for the dependent variable y. For example, if y = f (x) = 9x – 5 and x = 2, then we find y, or f (2), by replacing x with 2.
y = f (2) = 9 . 2 – 5
= 18 – 5
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,