# Understanding Function Notation

Functions are introduced as math studies get more abstract. The function takes an input value and produces an output value according to a rule. However, functions are just a new way of looking at familiar topics.

## Function Notation

While doing math, you might see something like this:

$f(x) = 5x - 4$

The left side f(x) looks like a monomial term of “f times x”. Instead, this is function notation and reads “f of x equals 5 times x minus 4”. One clue here is that the monomial “f times x” would typically be written as fx (without parentheses) or (fx) within parentheses.

## What “f” Means

The letter f is not a variable but rather a name for the function. Once a function is defined as above, later in a problem the function might simply be referred to by its letter name, f. A new function will be given a new letter, such as g(x)—read “g of x”.

## The Purpose of Functions

A function is a different way of referring to an equation. The equation $$y = 5x - 4$$ is immediately recognized as having a straight line graph. The graph of the function $$f(x) = 5x - 4$$ is the same line. Instead of being asked “for the equation $$y = 5x - 4$$ find the value of $$y$$ when $$x = 2$$” the equivalent question in “function language” is “for the function $$f(x) = 5x -4$$, find $$f(2)$$.”

## Evaluating Functions

The above function is evaluated the same way as an equation, by substituting 2 for $$x$$: $$5(2) - 4 = 6$$. Instead of reporting the answer as “$$y = 6$$”, the answer is “$$f(2) = 6$$”. The input value is $$2$$, and the output value is $$6$$.

Similarly, other problems given in function notation can be translated to more familiar terms.

Other examples:

Example 1: $$f(x) = 19 - 5x$$

Input the value $$4$$ for $$x$$: $$f(4) = 19 - 5(4)$$
The function outputs the value $$-1$$: $$f(4) = -1$$

Example 2: $$g(x) = 2x^2 -6$$

Input the value 7 for x :$$g(7)= 2(7)^2 - 6$$
$$g(7)=98-6$$
The function outputs the value 92: $$g(7)=92$$