7. Given that f(x) = {(1. 3), (2, 9), (5, 7), (11, 9)} and 90:) = {(218),(3,1).(4.5),(9, 1), (11, 0)} Determine the following. [5 marks] a- for) + 90') 90:) fOC) 1'06) X 906) g 905) fg(X) $09.05: Given that 90:) = %x + 9 and h(x) = (x + 1)(x 1), determine the following. Simplify where possible. a. h(x) g(x) [1 mark] h x 90:) [2 marks] 30:) [1 mark] 9 0 Mac) [2 marks] h o g(x) [2 marks] sneer State the domain and range of each function. Explain your thinking. a. f(x) = 3\\/2x + 8 1 [4 marks] b. g(x) = 5 cos(9[x 8031]) + 3 [3 marks] c. 2 log3(x2 5) + 1 [4 marks] Calculate the average rate of change for the function f(x) = 4x4 + 3x2 2x + 4 over the interval 2 S x S 1. f(x) is measured in litres, and x is measured in days. [4 marks] Use an interval of 0.001 to determine the instantaneous rate of change of the function 9(2) = 323 1222 + z 22 atz = 3. g(z) is measured in dollars, and z is measured in pages. Give your answer to the nearest tenth. [4 marks] fo) = 9x4 + 142x3 + 1029:2 13862: + 3 has a maximum or minimum at the points where x = 1.5 and where x = . Use instantaneous rates of change to verify this, and to classify each as a maximum or a minimum. [8 marks] Use algebra to determine whether each function is even, odd, or neither. a. f(x) = x cosx + 1 [3 marks] b. g(x) = ta\" [3 marks] x4- 8. A marine biologist measures the presence of a pollutant in an ocean and concludes that the concentration, C, in parts per million (ppm) as a function of the population, P, of the neighbouring town is given by C(P) = 1.38P + 97.4. The population of the town, in thousands, can be modelled by P(t) = 120078): where t is the time in years since the first measurement. a. b. d. Determine an equation, in simplified form, for the concentration of pollutant as a function ofthe number of years since the first measurement. [3 marks] What reasonable restrictions should be placed on the function's domain and range? [2 marks] The first measurement was taken in January 2018. Adapt the formula in part (a) to create an equation for the concentration as a function of the number of months since January 2020. [3 marks] In which year will the concentration reach 180 ppm? [3 marks] 9. In this course, we investigated polynomial, rational, exponential, logarithmic, sinusoidal, and other trigonometric functions. In your own words, describe a key feature of each type of function that differentiates it from the others. [6 marks] 10. Rod says that he is thinking of two functions that have the following characteristics: a. b. c. d. e. One is rational, and has ay-intercept at -2 One is trigonometric, and does not include the cosine function One contains the digit \"3\" and the other does not. Both have an instantaneous rate of change of 1.23 (rounded to two decimal places) at x = 2 The two functions intersect at x = 2 Provide one example of a pair of functions that meet Rod's criteria. Explain your thought process in making the functions, a screenshot, and calculations to verify each criterion. [7 marks]