Find the amplitude and period of the function. 56 y = 3 cos amplitude period Sketch the graph of the function. y y 4 12 -16 х-12 л8л -4л 8л 12л Д6л y y 4 4 2 -167-12 7 87 -4/n 8 12 л 16 л -16 12 -87 -4 7 4 7 87 12 n/16 A -2
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- Consider the function f(x)=2sin(pi/2(x-3))+6 state the amplitude a period p and midline state the base shift and vertical translation in the full period [0,P] state the maximum and minimum y values and their corresponding x valuesconsider the function f(t) = -4/5sin(3t-π/2) a) What is the amplitude of f(t)? b) what is the period of f(t)? C) what is the phase shift? d) Carefully sketch one period of f(t). Be sure to label four sub-intervals. e) Now carefully sketch one period of g(t)= -4/5 csc(3t-π/2). Be sure to label four sub-intervals and asymptotes.Determine the amplitude and period of the function y = -4cos 1/2x. Then graph one period of the function.
- A water wheel has a broken bucket like in the diagram below.The height of the broken bucket, in meters, above the surface of the water, y, after x seconds can bemodeled by the function shown below. y = 3.2sin(0.42x - 2.1) +1.9 5. In each rotation, the length of time that the broken bucket is visible above the surface of the water can befound by analyzing theA. y-interceptB. period of the functionC. difference between the two smallest positive x-interceptsD. difference between the maximum value and the minimum value of the functionA water wheel has a broken bucket like in the diagram below.The height of the broken bucket, in meters, above the surface of the water, y, after x seconds can bemodeled by the function shown below. y = 3.2sin(0.42x - 2.1) +1.9 5. In each rotation, the length of time that the broken bucket is visible above the surface of the water can befound by analyzing theA. y-interceptB. period of the functionC. difference between the two smallest positive x-interceptsD. difference between the maximum value and the minimum value of the function 6. The diameter of the water wheel is the A. y-interceptB. period of the functionC. difference between the two smallest positive x-interceptsD. difference between the maximum value and the minimum value of the functionThe graph of a periodic function ff is shown below. θθ 1.57 3.14 4.71 −1.57 f(θ)f(θ) 1 2 3 −1 −2 −3 What is the period of this function? What is the amplitude of this function? Write a function formula for f. (Enter "theta" for θ.)
- (1) Find the period of the function (2) Find the amplitude (3) Graph the following function over a two-period interval.Find period, amplitude, and midline of the following function: y=−16cos(4πx+4)−1 (a) The period of the graph is (b) The midline of the graph is y= (c) The amplitude of the graph isLet d be the distance in centimeters from the ceiling to the weight, when the weight is motionless, d=10. If the weight is disturbed, it begins to bob up and down or oscillate. Then d is a periodic furetion of t, time in seconds, so d=f(t). Determine the midline, period, amplitude, and the maximum and minimum values of f from the graph. Interpret these quantities physically; that is, use them to describe the motion of the weight (cm)