For each function, give the amplitude, period, vertical transl...

Question

For each function, give the amplitude, period, vertical translation, and phase shift, as applicable.

y = tan 3x

Accepted Answer

Welcome back. Everyone. In this problem, we want to find the amplitude period, vertical translation and phase shift for the function Y equals the tangent of seven X. For our answer choices, all of our answers say that the amplitude phase shift and vertical shifts are known. While A says the period is Pi B says the period is 1/14 of pi C says the period is 2/7 of Pi and D says it's 1/7 of pi. Now, if we're going to find these parts of our trigonometric function, it helps to think about what we know about the tangent function. OK. And recall recall that for every tangent function it's written in the general form that says the tangent of B multiplied by X minus C plus D, OK. Where the period to peer at it is equal to pi divided by the absolute value of B OK. Our P shift equals C let's see equals face shift and D equals our vertical translation. OK? Or, or vertical shift. So if we can compare our function for the tangent to our general form, then we'll be able to find that information. So given our function which is the tangent of seven eggs. OK. Here we can see that the B which is the coefficient of either X or X minus C depending on if there's a phase shift, B is equal to seven. OK? And if B equals seven or the absolute value of B would also be seven, right? We can see that there's no space shift. Here, there's only an X term. So C equals zero and our tangent function is not adding any constant value. So D also equals zero. So this confirms then that our phase shift is none or vertical shift is none. But we can find a period here, we can find a period because since the period equals pi divided by B, then here the period for or graph is going to be equal to pi divided by seven or 1/7 of pi and the tangent function has no amplitude. Therefore, when we look back on our answer choices, the correct answer would be answer choice D where it says that the period is 1/7 of pi while there is no field shift, no vertical shift and no amplitude. Thanks for watching everyone. I hope this video helps.

For each function, give the amplitude, period, vertical translation, and phase shift, as applicable.
y = tan 3x

Key Concepts

Amplitude

Period

Phase Shift

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