NAME Math 103 Exam 2 retake 12 December 2008 100 points Instructions 1 This exam has 6 pages including this one which contain 8 problems and one bonus problem Please check that you have all of the pages 2 Answer all of the following questions clearly and completely Justify all of your answers 3 You may not use a book or any notes for this exam 4 Give your answer to each problem completely and clearly in the space provided You may use the back of the exam pages for scratch work however if you want this work to be considered make note of it in the space provided for the problem 5 Erase or cross out work you do not wish to be graded 6 Credit partial or full will be given only if sufficient steps leading to the answers are shown 7 You have 50 minutes to complete this exam Page 1 Problem 1 17 points Let f x 4x3 12x2 7x 15 a 3 points What is the maximum possible number of zeros f may have Why b 8 points Find all possible rational zeros of f You do not have to test them to see if they re actually zeros c 6 points Without graphing prove that f must have a zero somewhere between x 3 and x 4 Problem 2 10 points Let f x 9x5 3x 2 and g x 4 x Find f g x You do not have to simplify Page 2 Problem 3 10 points Let f be the piecewise defined function given by f x 2 x 4 if x 0 x if 0 x 4 Graph y f x y 5 4 3 2 1 5 4 3 2 1 1 2 3 4 5 x 1 2 3 4 5 Problem 4 10 points Give a polynomial function h x that satisfies all of the following conditions The zeros of h are x 1 and x 3 and no other real values of x The graph of h crosses the x axis at x 1 but just touches the x axis at x 3 The degree of h is at least 5 You do not need to simplify your expression for h Page 3 Problem 5 16 points You have a total of 1800 feet of fencing You want to build a rectangular corral with two halves as shown in the picture below w h a 5 points Write an equation that relates the variables w and h Hint Use the fact that the total length of the fencing should be 1800 feet b 5 points Express the total area A of the corral both halves together as a function of w Hint Your answer from part a should help you c 2 points You should have a quadratic function as your answer to part b Its graph is a parabola Does this parabola open up or open down Why d 4 points What dimensions w and h will give you the largest enclosed area Page 4 Problem 6 20 points Here we go again Let R x x 4 3x 1 x 1 x 4 a 3 points What is the domain of R b 3 points If 0 is in the domain of R what is the y intercept of R c 3 points Write R in lowest terms d 3 points Find the x intercept s of R e 4 points Find any vertical asymptotes of R f 4 points Find the horizontal or oblique asymptote of R Page 5 Problem 7 5 points Is the following graph the graph of a function If so what function If not why not y 5 4 2 1 2 1 2 3 4 6 x 2 3 Problem 8 12 points Solve the following inequality for x x 5 2 x 3 0 Bonus problem 3 points Explain why every polynomial of odd degree must have at least one real zero Hint Think about the end behavior of the graph Page 6