New SAT Math Workbook

# For example substituting 0 3 and 3 for x gives us the

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Unformatted text preview: + 3 Then substitute x for f(x): g(f(x)) = x2 + 3 2 5. (D) 2 2 f(x2) = x , and ( f ( x ) ) = x . 2 Accordingly, f(x2) ÷ ( f ( x ) ) 4 x2 · 2 = 2. 2 x 2 2 x2 = ÷x 2 2 () 2 () 2 = The function is undefined for all values of x such that (x – 3)(x – 2) < 0 because the value of the function would be the square root of a negative number (not a real number). If (x – 3)(x – 2) < 0, then one binomial value must be negative while the other is positive. You obtain this result with any value of x greater than 2 but less than 3— that is, when 2 < x < 3. www.petersons.com Numbers and Operations, Algebra, and Functions 269 5. (C) If x = 0, then the value of the fraction is undefined; thus, 0 is outside the domain of x. However, the function can be defined for any other real-number value of x. (If x > 0, then applying the function yields a positive number; if x < 0, then applying the function yields a negative number.) Exercise 7 1. (E) After the first 2 years, an executive’s salary is raised from \$80,000 to \$81,000. After a total of 4 years, that salary is raised to \$82,000. Hence, two of the function’s (N,S) pairs are (2, \$81,000) and (4, \$82,000). Plugging both of these (N,S) pairs into each of the five equations, you see that only the equation in choice (E) holds (try plugging in additional pairs to confirm this result): (81,000) = (500)(2) + 80,000 (82,000) = (500)(4) + 80,000 (83,000) = (500)(6) + 80,000 2. (D) The points (4,–9) and (–2,6) both lie on the graph of g, which is a straight line. The question asks for the line’s y-intercept (the value of b in the general equation y = mx + b). First, determine the line’s slope: slope (m) = y2 − y1 6 − (−9) 15 = = =−5 x 2 − x1 2 −2 − 4 −6 5 In the general equation (y = mx + b), m = – 2 . To find the value of b, substitute either (x,y) value pair for x and y, then solve for b. Substituting the (x,y) pair (–2,6): y=−5x+b 2 6 = − 5 (−2) + b 2 6 = 5+ b 1= b 3. (B) In the xy-plane, the domain and range of any line other than a vertical or horizontal line is the set of all real numbers. Thus, option III (two vertical lines) is the only one of the thre...
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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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