1.3 Using Function Notation
Once we determine that a relationship is a function, we need to display and define the functional relationships so that we can understand and use them, and sometimes also so that we can program them into computers. There are various ways of representing functions. A standard function notation is one representation that facilitates working with functions.
To represent “height is a function of age,” we start by identifying the descriptive variables
Remember, we can use any letter to name the function; the notation
We can also give an algebraic expression as the input to a function. For example
Function Notation
The notation
Example 1: Using Function Notation for Days in a Month
Use function notation to represent a function whose input is the name of a month and output is the number of days in that month. Assume that the domain does not include leap years.
Analysis
Note that the inputs to a function do not have to be numbers; function inputs can be names of people, labels of geometric objects, or any other element that determines some kind of output. However, most of the functions we will work with in this book will have numbers as inputs and outputs.
Example 2: Interpreting Function Notation
A function
Example 3: Using Function Notation
Use function notation to express the weight of a pig in pounds as a function of its age in days
Question & Answer
Instead of a notation such as
Yes, this is often done, especially in applied subjects that use higher math, such as physics and engineering. However, in exploring math itself we like to maintain a distinction between a function such as
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