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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) = = sin _x +4 O h(x) = sin WIN * +4 O h (x ) = WIN sin - (x -4) O h(x ) = sin WIN (x-4)Describe a series of transformations that would transform fix) = (x| + 5 into g(x) =-2 x -1 Be sure to clearly communicate your reasoning using mathematical academic vocabulary.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) Oh(x) =A-x+3) Oh(x) = A(-x-3) O h(x) = -A(x-3)Find two possible non-linear functions g and h such that go h = sinx - x'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: A(1) = 50(0.5) What would be a suitable domain and range to view only the important features of this graph? Explain your reasoning.The graph of A(x) = ab" is shown below: 3+ 2 -5 4 3 2-1 1 2 3 4 + Which statement is TRUE about f (x)? There is a y-intercept at (0, -1). There is an asymptote at y = 0 O The range is all real numbers. O The domain consists of all x-values greater than -1.Q Which of the following functions represents discrete exponential decay? C .03 (1 ) A(t) = 27 1+ .03 12 O A(t ) = 27e 03 [1) .03 [1) A(t) = 27 1- .03 12 O A(t ) = 27e -0.03 (1)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.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/ - Vertical stretch by a factor of 2. O Horizontal stretch by a factor of 2.Describe how the graph of y = log W/ K 1 relates to the graph of y = log(x)