MAT 107 Final, Version A, Spring 2008 1) If (4, 4) is the endpoint of a line segment, and (2, 1) is its midpoint, find the other endpoint. A) (0, 7) B) (-2, 0) C) (8, 10) D) (0, -2) 2) Solve for x: A) - 4 3, 8 3 x 2 + 1-3 = 1 B) 8 3 C) - 8 3, 4 3 D) no real solution y + 8 3) Solve for y: y2 + 4y - 5-8 y2 + 10y + 25 = y - 8 y2 + 4y - 5 A) {11} B) {-88 } C) {-11 } D) no solution 4) Solve for x: x(6x - 5) = (6x + 1)(x - 2) A) {- 2} B) {- 1 3 } C) {- 2 } D) {6} 7 5) Solve the equation for x. The letters a, b, and c are constants. A) x = c ab B) x = c a + b C) x = ab c a x + b x = c, c 0 D) x = a + b c 6) Write 7 + 2i 6-3i in the standard form a + bi. A) 16 9-11 27 i B) 4 9-11 27 i C) 4 5 + 11 15 i D) 16 5 + 3 5 i 7) Solve 3k - 7-5 > 4. Express your answer using interval notation. A) (-, - 2 3 ) (16, ) B) (16 3 3, ) C) (- 2 3, 16 3 ) D) (-, - 2 3 )
MAT 107 Final, Version A, Spring 2008, page 2 of 8 8) Find an equation for the line that contains the point (2, -5) and is parallel to the line 7x + 5y = 9. A) 7x - 5y = -11 B) 7x + 5y = -11 C) 5x + 7y = -5 D) 2x + 5y = 9 9) Find the center (h, k) and radius r of the circle with equation (x + 6)2 + (y - 5)2 = 4. A) (h, k) = (-6, 5); r = 2 B) (h, k) = (5, -6); r = 4 C) (h, k) = (5, -6); r = 2 D) (h, k) = (-6, 5); r = 4 10) Find the domain of the function f(x) = 18 - x. A) {x x 3 2} B) {x x 18} C) {x x 3 2} D) {x x 18} 11) Match the function with the graph that best describes the height of an animal as a function of time. A) B) C) D)
MAT 107 Final, Version A, Spring 2008, page 3 of 8 12) Use the partial graph shown and draw a complete graph so that it is symmetric with respect to the y-axis. A) B) C) D)
MAT 107 Final, Version A, Spring 2008, page 4 of 8 13) Find and simplify the difference quotient A) 3 + -4 h f(x) = 3x - 2. B) 3 C) 3 + f(x + h) - f(x), h 0, for the function h 6(x - 2) h D) 0 14) Use a graphing utility to graph the function f(x) = x4-5x3 + 3x2 + 9x - 3 over the interval (-5, 5) and approximate any local maxima and local minima. If necessary, round answers to two decimal places. A) local minimum at (-0.57, -6.12) local maximum at (1.32, 5.64) local minimum at (3, -3) C) local minimum at (-3, -3) local maximum at (-1.32, 5.64) local minimum at (0.57, -6.12) B) local minimum at (-0.61, -5.64) local maximum at (1.41, 6.12) local minimum at (3, -3) D) local minimum at (-1, -6) local maximum at (1, 6) local minimum at (3, -3) 15) The graph of a function f is given. For what numbers x is f(x) > 0? 100-100 100-100 A) [-100, -60), (70, 100) B) (- -60) C) (-60, 70) D) (-60, )
MAT 107 Final, Version A, Spring 2008, page 5 of 8 16) Use the graph to find the intervals on which it is increasing, decreasing, or constant. A) Decreasing on (-3, -2) and (2, 4); increasing on (-1, 1); constant on (-2, -1) and (1,2) B) Decreasing on (-3, -1) and (1, 4); increasing on (-2, 1) C) Decreasing on (-3, -2) and (2, 4); increasing on (-2, 2) D) Increasing on (-3, -2) and (2, 4); decreasing on (-1, 1); constant on (-2, -1) and (1,2) 17) The cost C, in dollars, to produce graphing calculators is given by the function C(x) = 57x + 4500, where x is the number of calculators produced. How many calculators can be produced if the cost is limited to $61,500? A) 1158 calculators B) 1280 calculators C) 1000 calculators D) 800 calculators 18) A wire of length 7x is bent into the shape of a square. Express the area A of the square as a function of x. A) A(x) = 49 16 x 2 B) A(x) = 7 4 x 2 C) A(x) = 1 16 x 2 D) A(x) = 49 8 x 2 19) Determine whether the quadratic function f(x) = 2x2 + 2x - 6 has a maximum value or a minimum value and then find that value. A) minimum; - 13 2 B) maximum; - 13 2 C) maximum; - 1 2 D) minimum; - 1 2
MAT 107 Final, Version A, Spring 2008, page 6 of 8 20) Solve: x - 4 x + 2 < 1. Express your answer using interval notation. A) (-, -2) or (4, ) B) (-, -2) C) (-2, 4) D) (-2, ) 21) Solve: (b + 6)(b + 5)(b - 1) < 0. Express your answer using interval notation. A) (1, ) B) (-, -5) C) (-6, -5) or (1, ) D) (-, -6) or (-5, 1) 22) Find the domain of the rational function f(x) = -2x(x + 2) 2x2-5x - 7. A) x x - 2 7, 1 B) x x - 7 2, 1 C) x x 2 7, -1 D) x x 7 2, -1 23) Determine which rational function R(x) has a graph that crosses the x-axis at -1, touches the x-axis at -4, has vertical asymptotes at x = -2 and x = 3, and has one horizontal asymptote at y = -2. A) R(x) = -(x + 1)(x + 4) 2 2(x - 2)2(x + 3) C) R(x) = -2(x + 1)(x + 4) 2 (x + 2)2(x - 3) -2(x + 1)(x + 4), x 2, -3 B) R(x) =, x -2, 3 (x + 2)(x - 3), x -2, 3 D) R(x) = -2(x -3)(x + 2) 2, x -4, -1 (x + 4)2(x +1) 24) List the potential rational zeros of the polynomial function f(x) = 6x4 + 2x3 - kx2 + 2, where k is an integer. A) ± 1 6, ± 1 3, ± 1 2, ± 2 3, ± 1, ± 2 B) ± 1 6, ± 1 3, ± 1 2, ± 2, ± 1, ± 2, ± 3 3 C) ± 1 2, ± 3 2, ± 1, ± 2, ± 3, ± 6 D) ± 1 6, ± 1 3, ± 1 2, ± 1, ± 2 25) Find (g f)(x) when f(x) = -3x + 5 and g(x) = 6x + 3 A) -18x + 14 B) 18x + 33 C) -18x - 27 D) -18x + 33
MAT 107 Final, Version A, Spring 2008, page 7 of 8 26) Given f(x) = x - 6 x A) 25 B) 7 13 and g(x) = x2 + 9, find (g f)(-2). C) 13 D) 145 16 27) Find the inverse of the function f(x) = 3x - 4 5 A) f-1(x) = 5x - 4 3 C) f-1(x) = 5 3x + 4 B) f-1(x) = 5x + 4 3 D) f-1(x) = 5 3x - 4 28) Solve: 2 (7-3x) = 1 4 A) {-3} B) 1 2 C) {1} D) {3} 29) Solve:log 6 (x - 2) = 2 A) {66} B) {38} C) {62} D) {34} 30) Write log 3 x5 y7 as the sum and/or difference of logarithms. Express powers as factors. A) 5 log 3 x + 7 log 3 y B) 5 7 log 3 C) 5 log 3 x - 7 log 3 y D) 7 log 3 y - 5 log 3 x x y 31) Use the Change-of-Base Formula and a calculator to evaluate log 6 10.78. Round your answer to three decimal places. A) 0.754 B) 1.797 C) 1.327 D) 1.033
MAT 107 Final, Version A, Spring 2008, page 8 of 8 32) The function D(h) = 8e-0.4h can be used to determine the milligrams D of a certain drug in a patient's bloodstream h hours after the drug has been given. How many milligrams (to two decimals) will be present after 5 hours? A) 0.2 mg B) 59.11 mg C) 6.29 mg D) 1.08 mg 33) The number of men dying of AIDS (in thousands) since 1987 is modeled by y = 17.3 + 10.06(ln x), where x represents the number of years after 1987. Use this model to predict the number of AIDS deaths among men in 1994. Express the answer rounded to the nearest hundred men. A) 26,000 B) 25,800 C) 36,900 D) 37,000 34) Solve the system 2x + 9y = -56 11x + 3y = 64 A) x = -3, y = 8 B) x = 8, y = -8 C) x = -8, y = 8 D) x = 11, y = -11 35) A middle school's baseball playing field is a square, 55 feet on a side. How far is it directly from home plate to second base (the diagonal of the square)? If necessary, round to the nearest foot. 36) Solve: x2 + x + 3 = 0 37) The graph of a function f is illustrated. Use the graph of f as the first step toward graphing the function F(x), where F(x) = f(x + 2) - 1.