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1. The function g (x) = sin(x) is transformed into the function /(*) by stretching vertically by a factor of WIN about the x-axis, stretching horizontally by a factor of about the y-axis, and translating up 4 units. Which of the following is the equation for h (x) ? O h(x)= WIN sin * +4 A O h( x)= sin * +4 O h(x) = WIN sin 4 ( x - 4 ) O h( x) = sin (x-4)2. Describe a series of transformations that would transform f(x) = |x| +5 into g(x) = -2/x| -1 Be sure to clearly communicate your reasoning using mathematical academic vocabulary.5. The graph of y =f(x) is reflected across the y-axis then translated three units to the right. Which equation shows the transformed function h(x)? O h(x) = -f(x+3) O h(x) =A-x+3) O h(x) = A-x-3) O h(x) = -A(x-3)6. Find two possible non-linear functions g and h such that go h = sinx -x? ) 1. Select the graph of the inverse function to the function displayed here: 20 -20 O O 30 20 O OQ Q 2. Consider the graph below of the function f(x): 5 5 10 Using the graph, what is the value of /"(2) O /() = Of (2) =13 O Cannot be determined. O /(2) = 16Q 3. A military drone travels according to the formula ag) -45:, where dis the distance traveled in miles and t is the time in hours. What is the meaning of (585)? O It takes the drone 585 hours to travel 13 miles. It takes the drone 13 hours to travel 585 miles. miles. A military drone travels at an average speed of 45 miles per hour. O A military drone travels at an average speed of 585 miles per hour.4. Is the function /\\*) = ** invertible? If so, find the inverse Toggle bookmark O fx ) is not invertible. Of()=4x5. Determine whether the given functions f(x) and g(() are inverses of one another. Justify your response. Axx+2 and g(x) = /3x+2 31. Oscar is driving for a taxi company where he earns a base pay of $250 per week and a 7% commission on the charges he collects from his customers per week. Write an expression to represent Oscar's profit, P, each week when he collects d dollars from his customers. O P = 250d + 7 O P = 7d+ 250 O P = 0.07+ 250d P = 0.07d+ 250Q 2. At what point does the exponential function overtake the linear function on the interval (0,co)? [Type your answer as an ordered pair with no spaces.] Ax) = 2x 8(x) = 2*Q 4. Consider the function (x) = 4 (3)" to answer the following questions. Part A - From just looking at the equation of the function, would you expect the average rate of change for this function to be positive or negative? Explain your reasoning. Part B - Find the average rate of change on the interval [0, 2]. Show all of your work.5. Which of these is not like the other? Explain. Option 1: {(1,2), (2,4), (3,8), (4,16), (5,32)} Option 2: 3 = 4(1.6) Option 3: 4x - 2=. *- 3y 3 - 2 - -5 - -2 1 2 3 4 -2 - -3 - Option 4: O Option 2 because it has a variable in the exponent where as the equations modeling the rest of the options do not. O Option 1 because it is a continuous function where as the rest of the functions are discrete. O Opton 3 because it is neither linear or exponential where as the rest of the options are either linear or exponential. O Option 3 because it is a linear function where as the other options are exponential functions.Q 3. How much better is the return on a 9% yearly interest rate investment that is compounded daily as opposed to compounded yearly? Show all of your reasoning to justify your answer.5. The trend in iPhones over the past decade shows that the average iPhone depreciates by 53% per year. This can be modeled by the equation () = , (1 - 0.53)' where t is in years. Manipulate this equation so that it models the value of the average iPhone after w weeks. O V(w) & V. (0.009) " O V(w) ~ V. (8.89) " O WW) & V. (0.9856) " O WW ) & V. (0. 47) WQ 3. The half-life of a particular drug is 6 hours. When given an adult dosage, the following function can be used to model the amount of drugs, d, in an adult's system over time t in hours: al" A() = 50(0.5) What would be a suitable domain and range to view only the important features of this graph? Explain your reasoning.Q 5. The graph of A(x) = ab" is shown below: 3 2+ -5 4 -3 -2 1 2 3 4 Which statement is TRUE about / (x)? O There is a y-intercept at (0, -1). There is an asymptote at y = 0 The range is all real numbers. O The domain consists of all x-values greater than -1.Q 3. Isabella, a teacher's assistant, is creating a quiz. After reviewing Isabella's quiz question below, what information is missing? When Xavier's son was born, he opened a bank account with a continuous interest rate of 3.5% so that he could use this money purchase his son a car. Xavier's goal is to have at least $20,000 in account by his son's 16th birthday. Find the amount of money in Xavier's account after 16 years? Will he have enough to buy his son a car? O the principal investment amount O Interest Rate O the time the money is invested the number of times that interest is compounded per yearQ4. Which of the following functions represents discrete exponential decay? O .03 (1) A(t ) = 27 1+ .03 12 O A(t ) = 27e 03 (1) O .03 (1) A(t) = 27 1 - -03 12 O A(t ) = 27e -0.03 [1)5. Hinata researched rabbit population in the area and created the following model to assist her in predicting how many rabbits would exist at t = 12, A(12) = 80e.0*(12) . What value represents the growth rate of rabbits in her model? O e O 80 O 12 O 0.046. A radioactive substance has a decay rate of 15% per year. If we initially have 7 grams, which of the following models will find the how many grams will remain in t years. O A(t) = 7e-0.15t O A(t ) = 70 15: O A(t) = 7else O A(t) = 7e-15:Q7. Amelia is running for school president and would like to spread her message as fast as possible. Help her by answering her questions below. Part A: If I tell two classmates, and my message continuously spreads 40% each day, how many people will know after t days? Help her create a model while explaining each step in the process and label each variable in context to his situation. Part B: How many people will know my message after 10 days? Explain your process so that she can replicate this for 15 days. Part C: We have 2352 students at my high school. I only have a 30 days to advertise my candidacy. Will I reach the student body by this time? Explain why or why not.9. A radioactive substance is safe to handle when there is less than 1 gram left of it. If the substance has a decay rate of 70% per year, how long will it be before a 125 g substance is safe to handle? O between 7 and 8 years O between 6 and 7 years O between 5 and 6 years between 1 and 2 years6. Select the description of the transformation from f(x) = log, (x) to g(x) = log (x). O Vertical stretch by a factor of 3. O Vertical stretch by a factor of N| - O Vertical stretch by a factor of 2. O Horizontal stretch by a factor of 2.Q 8. Describe how the graph of y = log W H - 1 relates to the graph of y = log(x)