Match each function in Column I with the appropriate descripti...

Question

Match each function in Column I with the appropriate description in Column II.

I

y = -4 sin(3x - 2)

II

A. amplitude = 2, period = π/2, phase shift = ¾

B. amplitude = 3, period = π, phase shift = 2

C. amplitude = 4, period = 2π/3, phase shift = ⅔

D. amplitude = 2, period = 2π/3, phase shift = 4⁄3

Accepted Answer

Welcome back everyone. In this problem, we want to find the amplitude period and phase shift of the trigonometric function Y equals negative 14 multiplied by the sine of seven X minus five. For our answer choices, A says the amplitude is seven, the period is 1/7 of pi and the phase shift is 5/7 units to the left B says the amplitude is seven. The period is 1/7 of pi and the phase shift is seven fifth units to the left C says the amplitude is 14. The period is 2/7 of pi and the phase shift is five units to the right. And this says the amplitude is 14. The period is 2/7 of pi and the phase shift is 5/7 units to the right. Now, if we're going to figure out these parameters, OK. From our equation, it helps to think about what other sine functions look like. Now, what do we know about the sine function when we can? That every sign function is written in the form a multiplied by the sign of BX minus C plus D. OK. Where the coefficient of sine A is the functions amplitude OK. Or rather the amplitude is the magnitude of it. To be specific B helps us to find a period of our sine function. Because the period of the sine function will be two pi divided by the magnitude of BC helps us to find our phase shift because the phase shift is equal to C divided by B and the deal by itself. Let me, let me clear this here. B tells us the vertical shift off or graph. OK. So that means then that if we can compare our function to the general form, we should be able to find the values of ABC and D and thus figure out the amplitude period phase shift and or vertical shift. So let's try and figure that out. So let's take our function. OK? And our function was Y equals negative 14 multiplied by the sine of seven X minus five. Now, when we compare both, we compare both equations, we can tell that our equation is basically in the general form. OK? And since it's in the general form, by comparison, we can now tell that a, the coefficient of the sine function equals negative 14 B, the coefficient of X equals seven, see equals five. That is the term inside or of a sine. And here there is no constant being added to the sine function. So D would be equal to zero. That means there'd be no vertical shift now that we have the values of A B and C. That means we can go ahead to find the amplitude period and phase shift because no, this tells us then that the amplitude which equals the magnitude of our verified a magnitude of negative 14 would be equal to 14. Next, it tells us that our period, OK. Our period is going to be equal to two pi divided by B the magnitude of B which is seven. In other words, it's going to be 2/7 of pie. And finally, or fear shift, first shift is going to be equal to C which is five divided by B which is seven since our value is positive, that means we're moving to the right. So our phase shift is 5/7 units to the right. So here we found our amplitude to be 14, our period to be 2/7 of pi and our phase shift to be 5/7 units to the right. If we were to look back on our answer choices, that would have been answer choice. D thanks for watching everyone. I hope this video helped.

Key Concepts

Amplitude

Period

Phase Shift

Watch next

Match each function in Column I with the appropriate description in Column II.Iy = -4 sin(3x - 2)IIA. amplitude = 2, period = π/2, phase shift = ¾B. amplitude = 3, period = π, phase shift = 2C. amplitude = 4, period = 2π/3, phase shift = ⅔D. amplitude = 2, period = 2π/3, phase shift = 4⁄3

Key Concepts

Amplitude

Period

Phase Shift

Watch next