4.1.3 Writing Function Rules (continued)
Example 2 Function Notation
An algebraic expression that defines a function is called a function rule. If x is the independent variable in a function rule and y is the dependent variable, then the function notation for y is f ( x ), read as “ f of x ,” where f names the function. If an equation in two variables describes a function, then that equation can be written using function notation. For example, the equation y = 5 x + 2 can be written in function notation as f ( x ) = 5 x + 2. So, f (x) replaces y in the equation. Other letters can be used to name a function. For example, g ( x ) = 1 − x is another way of writing the equation y = 1 − x , which names the function g . To evaluate a function for a given input value, substitute that input value for x and then simplify, as demonstrated in Example 2.
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