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MAC 1105 Spring 2011 Mini-Term A Exam #4 Name___________________________________ MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval notation. 1) x2 - 5x ≥ -4 1) -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 A) [4, ∞) -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 B) (-∞, 1] -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 C) (-∞, 1] ∪ [4, ∞) -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 D) [1, 4] -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 2) (x - 3)(x - 4)(x - 6) < 0 2) -10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 A) (3, 4) ∪ (6, ∞) -10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 B) (-∞, 3) ∪ (4, 6) -10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 C) (6, ∞) -10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 D) (-∞, 4) -10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 1A Solve the rational inequality and graph the solution set on a real number line. Express the solution set in interval notation. x 3) ≥ 2 3) x + 3 -10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 A) (-∞, -6] or (-3, ∞) B) (-3, 6] -10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 -10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 C) (-∞, -3) or [0, ∞) D) [-6, -3) -10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 4) -10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 (x - 1)(3 - x) ≤ 0 (x - 2)2 -12 -10 -8 -6 4) -4 -2 0 2 4 6 8 10 12 A) (-∞, -3] ∪ (-2, -1) ∪ [1, ∞) -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 -4 -2 0 2 4 6 8 10 12 -4 -2 0 2 4 6 8 10 12 -2 0 2 4 6 8 10 12 B) (-∞, 1) ∪ (3, ∞) -12 -10 -8 -6 C) (-∞, 1] ∪ [3, ∞) -12 -10 -8 -6 D) (-∞, -3) ∪ (-1, ∞) -12 -10 -8 -6 -4 2A Graph the function by making a table of coordinates. 5) f(x) = 3 x 6 5) y 4 2 -6 -4 -2 2 4 6 x -2 -4 -6 A) B) 6 -6 -4 y 6 4 4 2 2 -2 2 4 6 x -6 -4 -2 -2 -2 -4 -4 -6 -6 C) y 2 4 6 x 2 4 6 x D) 6 -6 -4 y 6 4 4 2 2 -2 2 4 6 x -6 -4 -2 -2 -2 -4 -4 -6 -6 Write the equation in its equivalent exponential form. 6) log 216 = x 6 A) 216 6 = x B) x6 = 216 y 6) C) 6 x = 216 D) 216 x = 6 C) logb 1000 = 3 D) log1000 b = 3 Write the equation in its equivalent logarithmic form. 7) b3 = 1000 A) log3 1000 = b 7) B) logb 3 = 1000 3A Evaluate the expression without using a calculator. 8) log 125 5 1 A) 3 B) 3 9) log 8) C) 15 D) 1 1 4 64 9) B) -3 A) 3 C) 1 3 D) 12 10) log 2 8 10) A) 3 B) 1 C) 1 3 D) 6 Graph the function. 11) Use the graph of log x to obtain the graph of f(x) = -2 + log x. 2 2 11) y 10 5 -10 -5 5 10 x -5 -10 A) B) y -10 y 10 10 5 5 -5 5 10 x -10 -5 5 -5 -5 -10 -10 4A 10 x C) D) y -10 y 10 10 5 5 -5 5 10 x -10 -5 5 -5 -5 -10 -10 5A 10 x 12) Use the graph of f(x) = ln x to obtain the graph of g(x) = 3 - ln x. 12) y 5 -5 5 x -5 A) B) y y 5 5 -5 5 x -5 -5 5 x 5 x -5 C) D) y y 5 -5 5 5 x -5 -5 -5 Find the domain of the logarithmic function. 13) f(x) = log (x - 4) 3 A) (4, ∞) B) (-4, ∞) 13) C) (-∞, 0) or (0, ∞) 6A D) (-∞, 4) or (4, ∞) Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. 16 14) log2 14) x - 1 A) 4 - log2 x - 1 1 B) 4log2 2 - log2 (x - 1) 2 1 C) 4 - log2 (x - 1) 2 D) log2 16 - log2 x - 1 15) loga 3 x4 x + 5 (x -2)2 15) 1 A) 4 loga x + loga (x + 5) - 2 loga (x - 2) 3 B) 4 loga x - 3 loga (x + 5) - 2 loga ( x - 2) C) loga x4 + loga (x + 5)1/3 - loga (x - 2)2 D) loga x4 + loga (x + 5)-3 - loga (x - 2)2 Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions. 16) log 6 - log 2 16) 3 3 A) 1 B) log 4 C) log 6 1/2 D) log 12 3 3 3 17) 1 (log8 x + log8 y) - 2 log8 (x + 4) 5 5 5 x + y A) log8 (x + 4)2 17) 5 5 x + y B) log8 (x + 4)2 xy C) log8 2(x + 4) 5 D) log8 (x + 4)2 Use common logarithms or natural logarithms and a calculator to evaluate to four decimal places 18) log 21 9 A) 1.3856 B) 2.2765 C) 0.7217 D) 0.3680 If y varies directly as x, find the direct variation equation for the situation. 19) y = 9 when x = 63 1 C) y = 7x A) y = x + 54 B) y = x 7 Solve the problem. 20) If y varies directly as x, and y = 5 when x = 7, find y when x = 49. 5 7 343 A) B) C) 7 5 5 9 x B) y = 1 x 729 C) y = 7A 1 9x 18) 19) 1 D) y = x 9 20) D) 35 If y varies inversely as x, find the inverse variation equation for the situation. 1 21) y = when x = 81 9 A) y = xy 21) D) y = x 9 Solve the problem. 22) x varies inversely as y 2 , and x = 4 when y = 6. Find x when y = 2. A) x = 3 B) x = 48 C) x = 16 22) D) x = 36 Write an equation that expresses the relationship. Use k for the constant of proportionality. 23) P varies directly as the square of R and inversely as S. A) P = k + R2 - S2 B) P = kS C) P = kR2 S R2 Find the variation equation for the variation statement. 24) z varies jointly as y and the cube of x; z = 64 when x = 2 and y = -4 A) y = 2xy3 B) y = 2x3 y C) y = -2x3 y D) P = 23) kR2 S 24) D) y = -2xy3 Write an equation that expresses the relationship. Use k for the constant of proportionality. 25) P varies jointly as R and S and inversely as the square root of a. kRS k(R + S) RS kR B) P = C) P = D) P = A) P = a a k a S a 8A 25) Answer Key Testname: EXAM4A 1) C 2) B 3) D 4) C 5) B 6) C 7) C 8) A 9) B 10) C 11) B 12) B 13) A 14) C 15) A 16) A 17) D 18) A 19) B 20) D 21) A 22) D 23) D 24) C 25) B 9A