f (x) does not mean f times x. We can also think of a function as a machine—we put values into the machine, and the equation determines the values that come out. We can think of the function in Example 5b) like this: x 5 This value goes into the machine. f(5) 7 The value 7 comes out of f(x) x 2 f(5) 5 2 Function machine the machine. Sometimes, we call evaluating a function for a certain value fi nding a function value. EXAMPLE 6 In-Class Example 6 Let f (x) 4x 9 and g(x) x2 5x 4. Find the following function values. a) f (8) b) g(3) Answer: a) 23 b) 20 Let f (x) 5x 8 and g (x) x2 3x 1. Find the following function values. a) f (4) b) g (2) Solution a) “Find f (4)” means to fi nd the value of the function when x 4. Substitute 4 for x. f (x) 5x 8 f (4) 5(4) 8 20 8 12 f (4) 12 We can also say that the ordered pair (4, 12) satisfi es f (x) 5x 8. b) To fi nd g (2), substitute 2 for every x in the function g (x). g (x) x2 3x 1 g (2) (2)2 3(2) 1 4 6 1 11 g (2) 11 The ordered pair (2, 11) satisfi es g(x) x2 3x 1. Does this process “feel” any different from what you have already been doing? YOU TRY 5 Let f (x) 6x 5 and h(x) x2 9x 7. Find the following function values. a) f (1) b) f (3) c) h (2) d) h(0) 6 Solve Problems Using Functions The domain of a function does not have to be represented by x. When using functions to solve problems, we often choose a more “meaningful” letter to represent a quantity. The same is true for naming the function. 646 CHAPTER 10 Quadratic Equations www.mhhe.com/messersmith
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