Determine the magnitude and direction of the vertical shift and the phase shift for the function below.f(x) = sin(x + 7) +3Select the correct answer below:The vertical shift is 5 units up, and the phase shift is3units up, and the phase shift is 5 units to the right.O The vertical shift isO The vertical shift isπ-+53πunits to the left.units down, and the phase shift is 5 units to the left.3πO The vertical shift isunits down, and the phase shift is 5 units to the right.3units to the left.71RIO The vertical shift is 5 units down, and the phase shift isO The vertical shift is 5 units up, and the phase shift isunits to the right.3

Answered: Image /qna-images/answer/dd38fc67-1a66-416c-891b-baa09176d2a1.jpg

Answered: Determine the magnitude and direction…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.2: Trigonometric Equations

Problem 81E

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12C. Find the derivatives (1st of the ff. function or as specified in the problem. Simplify the expression in the lowest possible form)
a) Which function would you use to model f (x) without needing to use a phase shift?b) What is the amplitude, average, and period of f (x)?c) Let k(θ) = 2 sin( π/3 θ) + 8. What is the amplitude, average, and period of k(θ)?
9. The function y = -4 sin (3x + 6) - 1 shifts the graph 2 units to the right.TrueFalse
The metabolic rate of a person who has just eaten a meal tends to go up and then, after some time has passed, returns to a resting metabolic rate. This phenomenon is known as the thermic effect of food. Suppose that for one particular person, the thermic effect of food is given by the following equation, where F ( t ) is the thermic effect of food ( in kJ / hr ) and t is the number of hours that have elapsed since eating a meal. F ( t ) = - 10.35 + 175.8t e - t / 1.3 , for t > 0 a. Find F ' ( t ) . b. determine where the function F ( t ) is increasing and where it is decreasing. Interpret the answer. Upon eating a meal, does this person's metabolic rate begin to increase, or does it begin to decrease? After how many hours?
Find the amplitude, phase shift, and period of the function. y = −1/2cos(3x-π/4)+1 Give the exact values, not decimal approximations.
For the function f determine:(a) the amplitude, and hence a; (b) the period; (c) the constant k; (d) the phase shift, and hence b, and then(e) write down the equation that defines f.
Consider the function f(x) = 4sin(π/2 x) + 2 a. Find the first three positive values of x for which f(x) = 5. b. Find a function in terms of cosine that is equivalent to f.
A Ferris wheel has a radius of 10 m, and the bottom of the wheel passes 1 m above the ground. If the Ferris wheel makes one complete revolution every 22 s, find an equation that gives the height above the ground of a person on the Ferris wheel as a function of time. (Let y be the height above the ground in meters and let t be the time in seconds. Assume that when t = 0 the person is 11 m above the ground and going up.)

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