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MATH 1050-3: Exam 1 There are problems on both sides of each sheet. February 12, 2008 Name: Directions: To receive full credit, you must show all of your work. Write your answer in the space provided. Please box your answer and keep your work neat and organized. You may not use a calculator, notes, or any other electronic devices. If you need to use extra paper, please label the exercises appropriately so I can find them. If you finish early, take the time to check your answers. Relax, enjoy, and no cheating! (Cheating is punishable by a grade of 0%.) 1 1. For the points (−7, −4) and (2, 8), a) Find the distance between the points using the distance formula. b) Find the midpoint of the line segment joining the points using the midpoint formula. c) Find the equation of the line passing through the two points. Write this equation in slope intercept form. 2 2. Solve √ 3x − 5 = x − 1 for x. 3. Completely simplify the following: x2 −9 5x x2 −5x+6 10x2 3 4. Consider the function f (x) = q 9− 9 2 x. 25 a) What are the x and y intercepts? Make sure your answers are ordered pairs, not just numbers. b) What kind of symmetry does the function have? Use algebraic tests. c) What is the domain of the function? e) Draw a fully labeled graph of the function on the graph paper provided. 4 5. Consider the function f (x) = 3x−4 . 2x+1 a) Find f −1 (x), the inverse function of f . b) Find the domain and range of f and f −1 . 5 6. Consider the function g(x) = −(x + 3)3 − 2. a) Describe the vertical shifts, horizontal shifts, and reflections of this graph compared to the graph of f (x) = x3 . b) Graph g(x) on the graph paper provided. Please label your graph completely. 6 7. Given f (x) = 3x + 5 and g(x) = 2x2 − 7x + 9, find the following: a) ( fg )(x). What is the domain? b) (f ◦ g)(x). 7 8. Extra Credit:(Note that you must get this 100% correct to get the credit!) In one coordinate system (on the graph paper), carefully draw the graphs of √ f (x) = x and g(x) = −2f (3 − x) + 4. 8