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MA 103 Final Exam Review Sheet - Fall 2010

# MA 103 Final Exam Review Sheet - Fall 2010 - MONTGOMERY...

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MONTGOMERY COLLEGE GERMANTOWN CAMPUS MA 103 Final Exam Review Sheet (Revised Spring 2009) This is a review sheet. The actual final examination will be different. 1. Which of the following graphs i) Represents a function? Give a reason for your answer. ii) Represents a 1-1 function? Give a reason for your answer. a) -4 -2 0 2 y -4 -2 2 4 x b) -40 -20 0 20 -4 -2 2 4 x c) -4 -3 -2 -1 0 1

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2. Let the following be a graph of a function f . Sketch a graph of the line x y = and a graph 1 - f on the same set of axes. 3. Find an equation of the inverse of the function. 3 ( ) 1 f x x = + 4. a) If ( 29 3 7 x f x = - find ( 29 1 f x - b) If x x g 2 ) ( = find ( 29 1 g x - c) Below is the graph of ( 29 h x . Approximate ) 4 ( 1 - h 5. What are the domain and the range of the following function if the entire graph is shown? Express your answers using interval notation. 2 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
6. Find h and k such that 2 ( ) y x h k = - + is the equation whose graph is shown below. 7. Graph the following equation and write the exact coordinates of the vertex and x-intercepts. 2 ( ) 2 7 4 f x x x = - - 8. Find the vertex of the quadratic function by using the following three methods. 3 2 ) ( 2 + + = x x x f (a) Graphing (b) a b x 2 - = (c) Completing the square 9. Which of the following ordered pairs is a solution of the equation 2 2 1 x x y - - = , and which are not. Explain your answer. ( 29 2 , 1 - ( 29 7 , 2 - ( 29 1 , 0 ( 29 3 , 1 10. Which of the following relations represents a function, and which does not. Give a reason for your answer. A = {(2, 5),(4, 7),(7, 9),(8, 11)} B = {(1, 3),(2, 3),(2, 6),(3, 8)} 11. For 4 ) ( 2 - = x x f find and simplify ) 2 ( + t f . 12. Solve each equation for x . a) 14 5 2 = - x x b) 0 66 7 5 2 = - + x x c) 0 3 2 2 3 = - - x x x d) 0 16 3 = - x x e) 0 8 2 3 1 3 2 = - - x x f) 6 7 2 3 1 3 2 - = + x x 13. Use the discriminant to determine the number and type of solutions of the equation. 8 2 3 2 + - = x x 14. Solve the equation by completing the square. x x 10 4 2 = - 3

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15. The equation giving the height of an object thrown upwards starting at 12 feet above the ground is 2 16 40 12 ) ( t t t h - + = . a) When will the object reach its maximum height? b) What is its maximum height? c) When will the object hit the ground? 16. A company started business in 1995. Assume that the company has a profit per year given by the equation 37 . 2 56 . 2 19 . 0 ) ( 2 - + - = t t t f where ) ( t f represents the amount of profit in millions of dollars and t is the number of years since 1995. a) Use f to predict the amount of profit in 2003. b) Find t when 23 . 4 ) ( = t f . What do your results mean in terms of this company’s profits?
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