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1. Simplify. (2 marks each) a. 2V27 + 5V8 - 3V18 + 4v12 b. (2V/8 + 5V/12) 2. Find the inverse of the following function. Make sure you include any restrictions. Show all work. (6 marks) f (x) - -2V3x -1-5, x2- 3. The following graph is shown: a. Is the following relation a function? Justify your answer. (2 marks) b. Graph the inverse of the relation. Just submit the coordinates of the graph. (3 marks) c. Is the inverse a function? Justify your answer. (2 marks) 4. Consider the following equation: y - -2\\3x . 12 - 5. a. What is the base (original) function? (1 mark) b. Describe the series of transformations from the base function to y - -2v3x - 12 - 5. (3 marks) c. Write the equation in the function notation, y - af (k (x - d)) + c. (3 marks) 5. Simplify and state the restrictions if any. (5 marks) 2-25 27 2 15 6. Bob and Jack enter a 1000 km go-kart race. Bob drives 4 km/h faster than Jack does, but his go- kart gets a flat tire, which takes 30 minutes to repair. If both of them finish the race in a tie, how fast was each boy going during the race? (6 marks) 7. Tom and Kim are arguing about the following functions. Tom says that f and g are equivalent while Kim says that they can never be the same same since they do not have the same restrictions. Explain and justify their point of view, and explain who you think is correct. (5 marks). f(z) 32 14 24 5 g(z) -154: 22 8. To protect the endangered species, some leatherback sea turtles are introduced into a protected ecosystem. The following function models the population of leatherback sea turtles, P as a function of the time, t in years, since they are introduced in the protected ecosystem: (2 marks each). a. What is the initial number of leatherback sea turtles introduced into the protected ecosystem? b. Graph the population of leatherback sea turtles for the next 100 years. c. Determine the range of the model. d. How many leatherback sea turtles can be found in the protected ecosystem after 50 years? e. After how many years will there be 100 leatherback sea turtles? 50 + 16t P(t) - 2 + 0.1t