This assignment is out of 24 marks. To earn full marks for each question, a detailed algebraic solution and/or explanation is required. Review the "Directing Words" chart found in the course introduction. Complete all questions before submitting this assignment for grading. Please contact your teacher if you have any questions. 1. The graph of f (x) = x2 - 2 is transformed to y = f(x+1)+5. a. State the vertex of the graph of y = f (x ) and determine the vertex of the graph of the transformed function. (Recall that when the directing word "determine" is used, appropriate formulas, procedures and/or calculations need to be shown). (1 mark) b. The point (-4, 14) lies on the graph of y = f (x) . Determine the corresponding point on the transformed function. (1 mark) c. The point (0, 4) lies on the graph of the transformed function. Determine the corresponding point on the graph of the original function y = f (x) . (1 mark)2. The graph of y = f (x) is shown below. = A(x) a. On the grid above, sketch the graph of y = f- (x) +4 (1 mark) b. Describe the transformation(s) that occurred. Use the appropriate terms (translation, reflection and/or stretch) and identify any relevant axis or line of reflection with its equation. (1 mark) State the domain and range for y = f (x) using interval notation. (1 mark) d. Restrict the domain of y = f (x) so that the graph of y = f-(x) is a function. State the restriction using interval notation. (1 mark) N3. The graph of y = x2 has been transformed so that it has a vertex at (4,5) and passes through the point (2, -3). a. Sketch both parabolas on the grid provided. (1 mark) b. Determine the equation of the transformed function. (2 marks) 34. If the point (-5, -2) lies on the graph of 4y -4 = f -(x-1) , what is the corresponding point on the graph of y = f (x). (2 marks)5. The graph of a function y = a b(x - h) + k is shown below. Algebraically determine two different equations to represent this function. Hint: One equation should have a horizontal stretch and the other a vertical stretch. (3 marks) 56. A Ferris wheel has an approximate height of 150 metres and a 140-metre diameter. a. If the wheel rotates every three minutes, draw a graph which represent the height of a cart, in metres, as a function of time in minutes. Assume that the cart is at its lowest position at t=0. Show three complete cycles. (1 mark) b. Determine a sine function that models the height of a cabin for the duration of the ride. Recall that when the directing word "determine" is used, steps need to be shown and/or explained. Show a calculation or explain your process for finding each value a, b, c & d. Use radian values where applicable. (2 marks) 67. Given the graph of the function f (x) = -- 2 -3 (x + 1 ) 2 a. Give a step-by-step explanation of how to graph f (x) using transformations of the graph of y = - . (2 marks) b. State the domain and range using set notation. (1 mark) 8. Suppose that after entering the body, a substance is eliminated at a rate that can be modelled by the function C(t) =() where C is the concentration and t is time. Complete the following chart to match the scenarios as shown. (3 marks) Scenario Transformed Description of Transformation Equation A second substance delays the elimination of the first substance for 5 Horizontal translation 5 units units of time. C (1 ) = NI right. Instead of reducing the concentration of the substance to zero, the body reduces the concentration of the substance toward 4 units. The substance is eliminated at a third of the original rate. The initial concentration of the substance is doubled