1. The graph of f (x) = (x-3) is transformed to y = f(x+2)-5. a. State...

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1. The graph of f (x) = (x-3) is transformed to y = f(x+2)-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 (-1,16) 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. -2 1.5 0.5 -4 -35-3-2 -2 -1.5 -1 -0.5 0 0.5 1.5 2 2.5 3 3.5 -0.5 (-2.5,-0.5) -1 -1.5 a. On the grid above, sketch the inverse of y = f (x). (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 with its equation. (1 mark) C. State the domain and range this inverse graph using interval notation. (1 mark) d. Restrict the domain of y = f (x) so that the graph of the inverse is a function. State this new domain using interval notation. (1 mark) 3. The graph of y = x has been transformed so that it has a vertex at (-4,2) and passes through the point (-3,-1). a. Sketch both parabolas on the grid provided. (1 mark) b. Determine the equation of the transformed function. (2 marks) 4. If the point (-5,1) lies on the graph of 3y+3 = f ((x-4) 4), algebraically determine the corresponding point on the graph of y = f (x). (Hint: Work backwards.)(2 marks) 1. The graph of f (x) = (x-3) is transformed to y = f(x+2)-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 (-1,16) 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. -2 1.5 0.5 -4 -35-3-2 -2 -1.5 -1 -0.5 0 0.5 1.5 2 2.5 3 3.5 -0.5 (-2.5,-0.5) -1 -1.5 a. On the grid above, sketch the inverse of y = f (x). (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 with its equation. (1 mark) C. State the domain and range this inverse graph using interval notation. (1 mark) d. Restrict the domain of y = f (x) so that the graph of the inverse is a function. State this new domain using interval notation. (1 mark) 3. The graph of y = x has been transformed so that it has a vertex at (-4,2) and passes through the point (-3,-1). a. Sketch both parabolas on the grid provided. (1 mark) b. Determine the equation of the transformed function. (2 marks) 4. If the point (-5,1) lies on the graph of 3y+3 = f ((x-4) 4), algebraically determine the corresponding point on the graph of y = f (x). (Hint: Work backwards.)(2 marks)