Video: Finding the Amplitude of a Trigonometric Function from Its Rule

What is the amplitude of the function 𝑓(π‘₯) = π‘Ž sin (𝑏(π‘₯ βˆ’ β„Ž)) + π‘˜?

01:20

Video Transcript

What is the amplitude of the function 𝑓 π‘₯ is equal to π‘Ž sin of 𝑏 multiplied by π‘₯ minus β„Ž plus π‘˜?

Well, the first thing we want to do is actually, if we have a function in this form, is to identify what each part means. Well, we start on the right-hand side. And we’ve got plus π‘˜. Well, the plus π‘˜ is actually the vertical shift of our function. Moving along to the left, the β„Ž is actually the horizontal shift. And 𝑏 actually helps us to determine the period. And it does this because we have a formula. And that formula is that the period is equal to two πœ‹ over the absolute value of 𝑏. And so that’s how we use 𝑏 to find the period. We get that two πœ‹ because two πœ‹ is actually the period of the function sin π‘₯.

Okay, great. So we’ve got those three parts of this function determined. Now let’s look at the last part, π‘Ž. Well, we look at π‘Ž. So π‘Ž is actually the amplitude of our function. Okay, great. So now we actually know what each part tells us. To solve the problem, it says what is the amplitude of our function? Well, we get to the point. We could say that therefore, the amplitude of the function π‘Ž sin of 𝑏 multiplied by π‘₯ minus β„Ž plus π‘˜ is going to be π‘Ž.

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