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Function Notation

Function notation is a special way to write functions that explicitly shows that is a function of — in other words, that depends on Function notation is symbolically expressed as and read equals of Equations that are functions can be written using function notation.
Notice that has been replaced by In function notation, represents an element of the domain and represents the element of the range that corresponds to When written in function notation, the expression that describes how to convert an input into an output — the right-hand side expression — is called the function rule.
f(x)=-5x+4, the right-hand side expression is the function rule

Besides other letters such as or can be used to name the function. Similarly, letters other than can name the independent variable.


Interpreting Function Notation
To interpret an equation given in function notation, it is necessary to understand what both sides of mean. For example, consider the following equation.
Here, denotes that the function's input is and that is the output corresponding to this input.
Now, consider a different scenario. Let be a function that describes the number of words Kevin reads in minutes. The following statements are true for this function.
Here, is the number of words that Kevin reads in minutes and can be found by evaluating the function for However, the input is not a particular number in the second statement. In such cases, the statement can be interpreted as a question.
Based on the context, the second statement asks how many minutes it takes Kevin to read words. To find this value of the equation has to be solved for