New SAT Math Workbook

12 6 a b c d e 5 6 43 8 62 273 274 chapter 16 4 in

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Unformatted text preview: s are all multiples of 12, but no other elements. (B) The shaded region to the left of the y-axis accounts for all values of x that are less than or equal to –3 . In other words, this region is the graph of x ≤ –3. The shaded region to the right of the y-axis accounts for all values of x that are greater than or equal to 3 . In other words, this region is the graph of x ≥ 3. (C) Note that (–2)5 = –32. So, the answer to 1 3. 4. the problem must involve the number 5. However, the 2 in the number 2 is in the denominator, and you must move it to the numerator. Since a negative number reciprocates its base, − 1 5. (E) f ( 2) x +1 x +1 −5 = −32 . Substitute x + 1 for x, then simplify: 1 x +1 1 () 1= x +1 = 1= +1 1 x +1 1 + = 1+ ( x +1) x +1 1 x +1 = x +1 1 + ( x + 1) x + 2 www.petersons.com 272 Chapter 15 6. (C) According to the function, if x = 0, then y = 1. (The function’s range includes the number 1.) If you square any real number x other than 0, the result is a number greater than 0. Accordingly, for any non-zero value of x, 1 – x2 < 1. The range of the function includes 1 and all numbers less than 1. (C) The graph of f is a straight line, one point on which is (–6,–2). In the general equation y = mx + b, m = –2. To find the value of b, substitute the (x,y) value pair (–6,–2) for x and y, then solve for b: y = −2 x + b (−2) = −2(−6) + b −2 = 12 + b −14 = b 9. (A) The graph of any quadratic equation of the incomplete form x = ay2 (or y = ax2 ) is a parabola with vertex at the origin (0,0). Isolating x in the equation 3x = 2y2 shows that the equation is of that form: x= 2 y2 3 7. To confirm that the vertex of the graph of 2 y2 x= lies at (0,0), substitute some simple 3 values for y and solve for x in each case. For example, substituting 0, 1, and –1 for y gives us the three (x,y) pairs (0,0), ( 2 ,1), and ( 2 ,–1). 3 3 Plotting these three points on the xy-plane, then connecting them with a curved line, suffices to show a parabola with vertex (0,...
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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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