Unit 5 Polynomial Functions Assessment Unit 5: Polynomial Functions Learner Outcomes 1) Represent data, using polynomial functions (of degree ≤ 3), to solve problems Please choose one of the questions...

Polynomial Functions


Unit 5 Polynomial Functions Assessment Unit 5: Polynomial Functions Learner Outcomes 1) Represent data, using polynomial functions (of degree ≤ 3), to solve problems Please choose one of the questions below and record yourself explaining what strategies you used in solving the problem. Remember to use appropriate terminology and explain within the context of your question. Questions 1. Use the following graph of a polynomial function to answer the questions below. a) What is the domain and range of this function? (2 marks) b) What is the degree of this function? (1 marks) c) Is the leading coefficient positive or negative? Explain. (1 mark) d) What is the constant term of this function? (1 mark) 2. The tide depth in Deep Cove, British Columbia, from 4:00 to 15:00 on January 6, 2011, can be modelled accurately by the polynomial function: ?(?) = 0. 001? 3 − 0. 055?2 + 0. 845? + 0. 293 where f(t) is the tide depth in metres and t is the number of hours after midnight. a) What is the tide depth at 14:00 on January 6 (to the nearest tenth of a metre)? b) When is the tide depth the greatest on January 6? c) What are the restrictions on the variable t? Does this match the domain of the function? d) How would you use this data to determine the tide depth on January 7, 2011? 3. A 15-gallon tank is being filled with water and has a pump that will drain the tank when the amount of water inside the tank reaches a certain volume. The volume of water in the tank was measured in quarter-hour intervals, giving the following data: Time (hrs) 0 0.25 0.5 0.75 1 1.25 1.5 1.75 Volume (gallons) 6 7.125 8 8.625 9 9.125 9 8.625 a) What is the type of polynomial function that best fits the data? Explain your reasoning. (2 marks) b) Write the regression equation that represents the data. (1 mark) c) What is the volume at which the pump begins to drain the tank? (1 mark) d) How much time will have passed when the tank is empty? (1 mark) e) What are the restrictions on the volume and time? (2 marks)