228 CHAPTER 2 Graphs and Functions EXAMPLE 6 Using Function Notation Let ƒ1x2 = -x2 + 5x - 3 and g1x2 = 2x + 3. Find each of the following. (a) ƒ122 (b) ƒ1q2 (c) g1a + 12 SOLUTION (a) ƒ1x2 = -x2 + 5x - 3 ƒ122 = -22 + 5 # 2 - 3 Replace x with 2. ƒ122 = -4 + 10 - 3 Apply the exponent and multiply. ƒ122 = 3 Add and subtract. Thus, ƒ122 = 3, and the ordered pair 12, 32 belongs to ƒ. (b) ƒ1x2 = -x2 + 5x - 3 ƒ1q2 = -q2 + 5q - 3 Replace x with q. (c) g1x2 = 2x + 3 g1a + 12 = 21a + 12 + 3 Replace x with a + 1. g1a + 12 = 2a + 2 + 3 Distributive property g1a + 12 = 2a + 5 Add. The replacement of one variable with another variable or expression, as in parts (b) and (c), is important in later courses. S Now Try Exercises 51, 59, and 65. Be careful here. -22 = -1222 = -4 CAUTION The symbol ƒ1x2 does not indicate “ƒ times x,” but represents the y-value associated with the indicated x-value. As just shown, ƒ122 is the y-value that corresponds to the x-value 2 in ƒ. Function notation can be illustrated as follows. Name of the function Defining expression $1%1& y = ƒ1x2 = 3x - 5 Value of the function Name of the independent variable EXAMPLE 7 Using Function Notation For each function, find ƒ132. (a) ƒ1x2 = 3x - 7 (b) ƒ = 51-3, 52, 10, 32, 13, 12, 16, -126 (c) –2 3 10 6 5 12 f Domain Range (d) x y 0 2 4 2 4 y = f(x) Functions can be evaluated in a variety of ways, as shown in Example 7.
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