MA1210: Module 5 Polynomial and Rational Functions Lab 5.1 Rational Functions and Inequalities This lab requires you to find the maximum area, use synthetic division to find zeros of a polynomial, and use the remainder theorem to evaluate a polynomial function. Recommended Procedures: 1. (20 points) You have 150 yards of fencing to enclose a rectangular region. One side of the rectangle does not need fenced. a. Write the equation for area. b. Write the equation for the fencing. c. Solve the equation for fencing for y. d. Substitute what you got for Part c into the area equation for y. e. Write the function in the form () = 2 + + . f. Calculate 2 if the function has a maximum value at a < 0. g. Find the length of side y. h. Find the total area. 2. (10 points) Among all pairs of numbers whose sum is 24, find a pair whose product is as large as possible. What is the minimum product? 3. (15 points) Find all the roots/zeros of the equation 2 3 3 2 45 54 = 0. a. Use synthetic division to divide (2 3 3 2 45 54) by ( + 3). b. Divide the answer obtained in Part a by ( - 6) using synthetic division. 4. (10 points) Use the Remainder Theorem to find (4) for the equation () = 2 3 3 2 45 54. 1 MA1210: Module 5 Polynomial and Rational Functions Lab 5.1 Rational Functions and Inequalities 5. (15 points) Find the horizontal asymptotes, if any, of the rational functions. 12 2 a. () = 3+1 b. () = 32 +1 12 2 12 c. () = 3 2 +1 6. (10 points) If you are given the equation of a rational function, explain how to find the vertical asymptotes, if any, of the function's graph. 7. (20 points) Complete the required adaptive activities in ALEKS. Submission Requirements: Your lab report will be a Word document. Be sure you have answered each question correctly before final submission for grading. Include a header containing your name and the date on each page. Name the document MA1210_nn_Lab51.docx, replacing nn with your initials. Use Arial 12-point font and double-line spacing. Evaluation Criteria: Your submission will be evaluated against the following criteria: Did you complete the required adaptive activities in ALEKS? Did you answer all the questions correctly? Did you write the correct equations relating to the problem? Did you correctly execute the synthetic division problem? Did you correctly use the remainder theorem? Did you submit the answers in an organized fashion that was legible and easy to follow? Did you show all the steps in your answers? 2