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POLYNOMIAL & RATIONAL FUNCTIONS (1.6) NAME_______________________________ 1. Consider the function y( x) x6 2 x5 8x 4 14 x3 11x 2 28 x 12 A. Plot y ( x) in the window 3 x 4 , 50 y 100 . -3 -2 -1 0 1 2 3 4 B. Find the zeros of y ( x) . C. Express y ( x) in factored form. 2. Create a possible equation for the polynomial graphed below. Include the sign of the leading coefficient. -6 -5 -4 -3 -2 -1 0 1 2 3 4 3. Solve for h as a function of s and simplify: 5 s 8w0.25 h0.75 4. Create equations of rational functions with the following characteristics: A. A horizontal asymptote of y 2 and a vertical asymptote of x 4 . B. No horizontal and no vertical asymptotes. 5. Match the function expressed in words with a graph and an equation. Find the horizontal asymptote for each, A. Average cost of producing x items. B. The oxygen content in a lake after dumping in fertilizer as a function of time. (The oxygen content decreases at first, but then returns to its previous level.) C. The amount of a drug in a body as a function of time. (Assume the drug was given by injection.) D. The number of people purchasing a (trendy) new product as a function of time. E. The number of people getting a particular disease during an epidemic as a function of time. (i) y 25 x 2 5 x3 1 (ii) y 25 x 6 x 2 2 x 2 10 (iii) y 4 x2 x2 9 (iv) y a. b. 5 1.2 4 1 3 0.8 2 0.6 1 0.4 20 x 1000 x (v) y x2 x 1 x2 1 0.2 0 0 10 20 30 40 50 60 0 x 0 c. 2 4 6 8 10 d. 10 4.5 4 8 3.5 3 6 2.5 2 4 1.5 1 2 0.5 0 0 0 5 10 15 20 25 0 30 1 2 e. 1000 800 600 400 200 0 0 5 10 15 20 25 30 3 4