D. Function Notation

D. Function Notation

As you progress into more advanced mathematics, you will work with multiple functions at a time. Function notation is a way of writing the equations of functions in a more user-friendly fashion.

To write a linear equation in function notation, y in the equation is commonly replaced with f( x). When using function notation, the f( x) represents a single entity and it is read as "f of x ". It does not mean f × x.

For example «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»y«/mi»«mo»=«/mo»«mn»3«/mn»«mi»x«/mi»«mo»+«/mo»«mn»2«/mn»«/math» written in function notation is «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mn»3«/mn»«mi»x«/mi»«mo»+«/mo»«mn»2«/mn»«/math». Note that «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»y«/mi»«mo»=«/mo»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/math», so «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mn»3«/mn»«mi»x«/mi»«mo»+«/mo»«mn»2«/mn»«/math» represents the same function as «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»y«/mi»«mo»=«/mo»«mn»3«/mn»«mi»x«/mi»«mo»+«/mo»«mn»2«/mn»«/math».

Function notation allows you to determine the value of a specific function, or point on the graph of the function, by replacing x with the x-value of interest.

The following example uses function notation to determine function values (output values).

Example 1

Let «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»y«/mi»«mo»=«/mo»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/math». Rewrite the equation «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»y«/mi»«mo»=«/mo»«mn»2«/mn»«mi»x«/mi»«mo»+«/mo»«mn»3«/mn»«/math» using function notation. Evaluate . When the input is -5, the output is -7.

 

Most commonly, function notation is denoted by f(x). However, when referring to more than one function at a time, or when context would suggest the use of other variables, both f and x can be represented by other letters, such as g(x) or P(t).

Note that the variable within the brackets is always the input value, or domain, and the g(x), P(t), or f(x) will always be the generated output value, or range.