EXAMPLE 5 a) Evaluate y x 3 for x 2. b) If f (x) x 3, fi nd f (2). Solution a) To evaluate y x 3 for x 2 means to substitute 2 for x and fi nd the corresponding value of y. y x 3 y 2 3 Substitute 2 for x. y 5 When x 2, y 5. We can also say that the ordered pair (2, 5) satisfi es y x 3. b) To fi nd f(2) (read as “f of 2”) means to fi nd the value of the function when x 2. f (x) x 3 f (2) 2 3 Substitute 2 for x. f (2) 5 We can also say that the ordered pair (2, 5) satisfi es f (x) x 3 where the ordered pair represents (x, f (x)). Note Example 5 illustrates that evaluating y x 3 for x 2 and finding f(2) when f(x) x 3 is exactly the same thing. Remember, f(x) is another name for y. YOU TRY 5 a) Evaluate y 2x 4 for x 1. b) If f (x) 2x 4, fi nd f (1). 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. Notice that f(2) indicates that we replace the x-value with 2. f(x) does not mean f times x. 4 Find Function Values for Real-Number Values of the Variable Sometimes, we call evaluating a function for a certain value fi nding a function value. EXAMPLE 6 Let f (x) 6x 5 and g(x) x2 8x 3. Find the following function values. a) f (3) b) f (0) c) g(1) Solution a) “Find f(3)” means to fi nd the value of the function when x 3. Substitute 3 for x. f (x) 6x 5 f (3) 6(3) 5 18 5 13 f (3) 13 We can also say that the ordered pair (3, 13) satisfi es f (x) 6x 5. 204 CHAPTER 4 Linear Equations in Two Variables and Functions www.mhhe.com/messersmith
messersmith_power_intermediate_algebra_1e_ch4_7_10
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