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1. Determine the value of n so that the average rate of change of the function f(x) = x2 - 3x + 7 on the interval -5 s x S n is -1. [4] 2. Let f(x) = nx2 - 2x + 5 and g(x) = 6x2 - 5x + m. The functions are combined to form the new function h(x) = f(x) - g(x). Points (1, 2) and (-5, 10) satisfy the new function. Determine the exact values of m and n. [4]1. Given f(x) = x - 1 and g(x) = x + 3, fill out the table below. Sketch h(x), j(x), k(x), and I(x) in the set of axes below. Make sure to clearly label each function and your axes. Show your work in identifying the domain and range in the space below. [8] h(x) = f(x) + g(x) j(x) = f(x) - g(x) k(x) = f(x)g(x) I(x) = f(x)/g(x) the equation (fully simplified) domain range2. a) Describe a specific, real world scenario where an instantaneous rate of change is positive. [1] b) Describe a specific, real world scenario where an instantaneous rate of change can equal zero. [1] c) Describe a specific, real world scenario where an average rate of change can be negative. [1]1. As a tomado moves, its speed increases. The function Std) = 03logd + 65 relates the speed of the wind, 8, in miles per hour, near the centre of a tornado to the distance that the tornado has travelled, d, in miles. (a) Calculate the average rate of change for the speed of the wind at the centre of a tornado from: [3] (i) mile 10 to 100 (ii) mile 100 to 1000 (iii) Describe how the two rates above compare with respect to the given information. to} Estimate the instantaneous rate of change at d = 1000 miles. Use an interval of 0.01. Round your answer to the nearest hundredth. Do not nd the instantaneous rate of change using the difference quotient or anyr Calculus method. Explain what the value represents in this situation. [3] 2. Two rectangular lots are adjacent to each other, as shown in the diagram below. Using a function operation, determine how many times bigger the large lot is than the small lot. Clearly identify the individual component functions and simplified final equation. [3] 2x - 2 3x - 3 3. The price of 1 L of gasoline is $1.75. On a level road, Haithm's car uses 0.1 L of fuel for every kilometre driven. Using function composition, determine how much the gas costs to fuel the trip if Haithm drives 100 km. Clearly identify the individual component functions and simplified composite equation. [3]