New SAT Math Workbook

Depending on the functions rule and its domain the

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Unformatted text preview: (B) –1 (C) 0 (D) 1 (E) 2 What integer is equal to 4 3 2 + 4 3 2 ? 5. (E) 2. 1 4n + 4n + 4n + 4n = (A) 44n (B) 16n (C) 4(n · n · n · n) (D) 4(n+1) (E) 164n Which of the following expressions is a simplified form of (–2x2)4 ? (A) 16x8 (B) 8x6 (C) –8x8 (D) –16x6 (E) –16x8 3. Numbers and Operations, Algebra, and Functions 253 5. FUNCTION NOTATION In a function (or functional relationship), the value of one variable depends upon the value of, or is “a function of,” another variable. In mathematics, the relationship can be expressed in various forms. The new SAT uses the form y = f(x)—where y is a function of x. (Specific variables used may differ.) To find the value of the function for any value x, substitute the x-value for x wherever it appears in the function. Example: If f(x) = 2x – 6x, then what is the value of f(7) ? Solution: The correct answer is –28. First, you can combine 2x – 6x, which equals –4x. Then substitute (7) for x in the function: –4(7) = –28. Thus, f(7) = –28. A problem on the new SAT may ask you to find the value of a function for either a number value (such as 7, in which case the correct answer will also be a number value) or for a variable expression (such as 7x, in which case the correct answer will also contain the variable x). A more complex function problem might require you to apply two different functions or to apply the same function twice, as in the next example. Example: If f(x) = (A) (B) (C) (D) (E) Solution: The correct answer is (E). Apply the function to each of the two x-values (in the first instance, you’ll obtain a numerical value, while in the second instance you’ll obtain an variable expression: 2 2 1 f = = 1 = 2×4 =8 2 2 1 4 2 x2 , then f × f = 2 x 1 1 4x 1 8x 16x 1 4 x2 16x2 () 2 2 2 1 = = 2x 2 f = x 12 1 2 x x Then, combine the two results according to the operation specified in the question: 1 f × 2 1 f = 8 × 2 x 2 = 16 x 2 x 254 Chapter 15 Exercise 5...
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This note was uploaded on 08/15/2010 for the course MATH a4d4 taught by Professor Colon during the Spring '10 term at Embry-Riddle FL/AZ.

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