5 Use Function Notation We can use function notation to name functions. If a relation is a function, then f (x) can be used in place of y. f (x) is the same as y. For example, y x 2 is a function. We can also write y x 2 as f (x) x 2. They mean the same thing. Definition If y represents a function, then the function notation f (x) is the same as y. We read f (x) as “f of x,” and we can say y f (x). EXAMPLE 5 In-Class Example 5 a) Evaluate y 2x 5 for x 4. b) If f (x) 2x 5, find f (4). Answer: a) 3 b) 3 a) Evaluate y x 2 for x 5. b) If f (x) x 2, fi nd f (5). Solution a) To evaluate y x 2 for x 5 means to substitute 5 for x and fi nd the corresponding value of y. y x 2 y 5 2 Substitute 5 for x. y 7 When x 5, y 7. We can also say that the ordered pair (5, 7) satisfi es y x 2. b) To fi nd f (5) (read as “f of 5”) means to fi nd the value of the function when x 5. f (x) x 2 f (5) 5 2 Substitute 5 for x. f (5) 7 We can also say that the ordered pair (5, 7) satisfi es f (x) x 2 where the ordered pair represents (x, f (x)). Note Example 5 illustrates that evaluating y x 2 for x 5 and finding f (5) when f (x) x 2 are exactly the same thing. Remember, f (x) is another name for y. YOU TRY 4 a) Evaluate y 3x 7 for x 2. b) If f (x) 3x 7, fi nd f (2). Different letters can be used to name functions. g(x) is read as “g of x,” h(x) is read as “h of x,” and so on. Also, the function notation does not indicate multiplication; f (x) does not mean f times x. www.mhhe.com/messersmith SECTION 10.5 Introduction to Functions 645
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