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Test 2 fa 09 - Test 2 College Algebra Erika Noffsinger Fall...

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Unformatted text preview: Test # 2 / College Algebra Erika Noffsinger / Fall 2009 Name:_________________________________________________ Points Earned Points Possible 1. 2. 3. 4. 5. 6. 7. Extra Credit. 24 Points (3 each) 8 Points (2, 3, 3) 12 Points (2 each) 12 Points (2 each) 20 Points (4 each) 6 Points (4, 2) 18 Points (9 each) 4 Points Total:________________________________________(100+ Points) 1. If f(x) = 2x2 ‐12x + 10 answer the following questions: a) Write f(x) in vertex form? b) What is the vertex? Is it a maximum or minimum point? Why? c) What is the y –intercept and the point symmetrical to this point? d) What are the x‐intercept(s), if they exist? e) Graph f(x). f) What is the range of f(x)? g) Where is f(x) increasing and decreasing? h) When is f(x) > 0? Either use the graph or solve algebraically. 2. Let f(x) = x3 + 3x2 – 6x – 8 , answer the following questions: a) Find the possible rational zeros of f(x) by using the Rational Root Theorem. b) Find the zeros of f(x). c) Rewrite f(x) as a product of linear factors. 3. Let s(x) = – (x – 2)2(x + 3)(x + 1)3 a) What are the end behaviors of the graph of s(x)? As x As x ∞ ______________ ∞ ______________ b) What are the x‐intercepts? State their multiplicity. c) Does the graph cross or touch the x intercepts? Explain. d) What is the y – intercept? e) Sketch a general shape of s(x), plot any additional points, if needed, to see what is happening to the graph. f) By either using the graph of s(x) or solving algebraically, state which intervals s(x) > 0 and when s(x) < 0. 4. Let g(x) = x 9 x2 . Find the following where possible. a) Where are the vertical asymptote(s)? b) Does f(x) have a horizontal or a slant asymptote? Where is it? c) Depending on your answer on part b), does the graph cross the horizontal/slant asymptote? If so, where? d) What is the y‐intercept? e) What are the x‐intercept(s)? f) Graph the general sketch of f(x). Plot a couple of points on either side of the vertical asymptote(s) and x – intercept(s) to help you see what is going on with the graph. 5. Solve the following equations: a) 2 2x +1 = 8 b) e (x + 8) = 6 c) y = log 5 d) log(2x +1) ‐ log(3x – 1) = 1 e) log 2 (logx) = 2 1 25 6. Let f(x) = x 3 – 6x2 + 13x – 10. a. Use the fact that 2 + i is a zero of f(x) to find the remaining zeros of f(x). b. Write f(x) as a product of linear factors. 7. Choose only 2 of the following 4 word problems to do. Circle the two you want graded. Extra credit will not be given if you do more than 2 of the 4 word problems. A) An automobile manufacturer can produce up to 300 cars per day. The profit made from the sale of these vehicles can be modeled by the function P(x) = ‐10x2 + 3500x – 66,000, where P(x) is the profit in dollars and x is the number of automobiles made and sold. Based on this model: a) Find the y – intercept and explain what it means in this context. b) Find the x – intercepts and explain what they mean in this context. c) How many cars should be made and sold to maximize profit? d) What is the maximum profit? B) In Biology class you are doing a lab watching a particular bacteria, the teacher tells you that the growth of the bacteria is exponential. (Hint: Let t=0 be the initial amount of bacteria.) a) When you started the lab there was a population of 175. After five hours, the bacteria grew to a population of 1055. Find the function to model the growth of the bacteria. b) What is the population of the bacteria after 24 hours? c) How long will it take the population to double? Write your answer in hours, minutes and seconds. C) You won the Lottery!!! You decide to invest your winnings of $150,000 for 5 years. You are not sure if you will get a better return on your investment if you invest it at rate of 6.25% compounded twice a year or if you invest at a rate of 5.95% compounded continuously. a) Which investment would give you a greater return? b) How long would you have to invest the $150,000 at the investment of 5.95% compounded continuously to get a return of $279,000? D) The drug Lorazepam, used to relieve anxiety and nervousness, has a half‐life of 14 hours. The doctor prescribed one 2.5 milligram tablet every 24 hours. a) Write an equation that represents the amount of Lorazepam left in the bloodstream after t hours of taking the medication. b) What percentage of the last dosage remains in the patient’s body when the next dosage is taken? c) If the doctor wants the patient to take the next dose when there is 1.25 milligrams in the bloodstream then how often should the patient take one 2.5 milligram tablet Extra Credit: Find the inverse of g(x) = log 2(x + 2) – 3. ...
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