Honors Precalculus - Module 4 Project 1. Given the function defined by y = 3-6 sin| 2x+ 2 determine the solution to each question below. Show your work and explain how you determine each characteristic of the function. a. What is its period? b. What is the amplitude of its graph? c. What is its domain and range? d. What is the y-intercept of its graph? e. What is its phase shift? f. Sketch two periods of the graph of this function. Label the axes with key values. 2. The average high monthly temperature (in degrees Fahrenheit) in Duluth, Minnesota, is shown in the table. A scatterplot of the data is also given. a. Determine a function of the form f(x) = a sin b(x - c) + d, where a, b, c, and d are constants, that models the data. Show the work necessary in determining the values. Do not use regression capabilities of your graphing calculator. b. Determine the average high monthly temperature in Duluth 100+ 90 70- 60- 50 20- 10- -10+ 2 Month Deg. F. Month Deg. F. Jan 21 July 75 Feb 26 Aug 74 Mar 35 Sept 65 Apr 46 Oct 52 May 56 Nov 38 June 66 Dec 25 + 4 6 8 10 12 14 16 3. The rabbit population on Park Point in Duluth, MN at time t is modeled by r(t) = = 225cost+425 where t is measured in years. (Park Point, by the way, is reported as the world's longest freshwater sand spit) a. What is the maximum number of rabbits on Park Point during a population cycle? b. How long is the population cycle? c. Find the approximate number of rabbits on the island after 3.2 years. d. Sketch a graph of the first period of this function, marking key axis values. e. Solve algebraically: in what year(s) during the first population cycle will the number of rabbits be equal to 500?