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Part 1.3

2.3 Assignment 2: Problem Set Overview In this assignment you will be completing problems based on graphing and modeling polynomial functions. The purpose of this assignment is to practice graphing and modeling polynomial functions. As you work, show your thinking in the box below. Problem Sets Questions Solve the questions below. Show your work. 1. A third degree polynomial function f has real zeros -2, 2, and 3, and its leading coefficient is negative Write an equation for f. Sketch the graph of f. How many different polynomial function are possible for f? 2. Write the polynomial and sketch the graph of a fifth degree polynomial function whose leading coefficient is positive 1 and has zeros of 4 multiplicity 2 and 0 multiplicity 33. The graph of one of the following functions is shown below. Identify the function shown in the graph and explain why the other is not the correct function. a. y = x (x + 2)(x - 3 b. y = x(x+ 2)(x - 3)\fUse the following table to answer questions 4 and 5. Interval Value of f (x) (- 00, - 2) Positive (- 2, 1) Negative (1, 4) Negative (4, 00) Positive 4. What are three real zeros of the polynomial function f? 5. Can the degree of f ever be odd? Explain?1.3: Problem Set Overview In this assignment you will be completing problems based on modeling parent functions. The purpose of this assignment is to practice modeling functions based on real world scenarios. As you work, show your thinking in the box below. Problem Sets Questions Solve the questions below. Show your work. 1. The cost of a cell phone service can be modeled by the equation C(m) = 5m + 23. 42 where C(m) is the total cost for m minutes of cell phone use. State the meaning of the slope and y-intercept of this function with respect to the costs associated with the cell phone service. 2. Using the parent function y = 3", write the equation of an exponential function that is flipped over the X-axis, shifted 3 to the right and 4 down.Z 3. The graph of a parent function is shown below. Sketch the graph of the transformed function if the new image is represented by the function f(x) : xl'x + 2. 4. The number of cars C a car dealer sells in each month of the year from January to October can be modeled by the function B = 15|t 5| + 100 where t is thetime in months and t = 1 represents January. What is the maximum number of sales in one month? In what month is the maximum reached? 5. A city's population has been recorded over a period of ten years. The data shows a constant growth between each year. Which function type would you use to model this situation? Explain why the function type you chose is the best option.2.2: Problem Set Overview In this assignment you will be completing problems based on finding real and complex zeros of polynomials. The purpose of this assignment is to practice using different methods to find real and complex zeros of polynomials. As you work, show your thinking in the box below. Problem Sets Questions Solve the questions below. Show your work. 1. Sketch a graph of the following polynomial. Show all x-intercepts. y: -2(.\\- + 3)(.\\' 0.5)(.\\' + 1) 5 2. Given that 2 i + 2 is a zero off(x) = x , 6x4 + 11x3 2 x2 , 14x + 5, find all complex roots using 3 nthetic division. List our ossible rational roots also. 3. Determine k so that f (x) = x - 11x + kx - 4 has x - 2 as a factor. 4. True or False. If False, explain why or provide a counterexample A polynomial of the 5th degree can have only 2 real roots and 3 imaginary roots 5. A polynomial P(x) has the following roots: - 2, 1 + 3i, 5i. Write an equation of the function of lowest possible degree and use that to find the particular equation if P(0) = 25