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y=Asin(B(x+C))+D a. State the amplitude, vertical displacement, period, and the phase shift. A. State the amplitude, vertical displacement, period, and the phase shift. vertical deppacement D=1, upward Period =B2π=2π/151π=2π15 6b. State the formula for the maximum and minimum value of g(x). 152(x−3)=(24n−1)n is an integer
7. If f(θ)=tanθ is transformed to g(θ)=atan[b(θ−c)]+d by a vertical compression by a factor of 21, Horizontally expanded by a factor of 4 , then translated π units right and 1 unit down. a. What is g(θ) ? g(θ)=atan(b(θ−c))+d b. It is known that the point P(4π,1) is on f(θ). What is the image of P under the given transformations? g(4π)=21tan(4(4π−π))+1 =21tan(π−4π)+1=0+1 =1/2tan(−3π)+1g(4π)=1 c. What are the equations of the asymptotes for the function g(θ) for all θ ? x=1x=2x=nx(n∈−∞,∞) d. State the period of g(θ). g(θ)=42π=2π
9. A Ferris wheel has a radius of 30 m. Its center is at 32 m above the ground. it fotates ofice every 15 s. Suppose you get on the bottom at t=0. Write an equation that expresses your he shit as a function of elapsed time. - Radrut of whet = anpli Va. Sketch a graph of the height as you ride the wheel. - Veviod = one votation, lowest phit: (32−30)=2m Wighelt poid: (32+30)=42 m h(t)=30sin(52πt−2π)+32 - suofr : C=213 - Ventical shift = cadi b. Write an equation using sine and another equation using cosine.