Fill in the blank(s) to correctly complete each sentence.

Question

The graph of y = 4 sin x is obtained by stretching the graph of y = sin x vertically by a factor of ________.

Accepted Answer

Welcome back everyone. In this problem, we want to figure out which of the following statements correctly describes the procedure for obtaining the graph of Y equals 20 sine X from the graph of Y equals sine X. For our answer choices, A says to translate the graph of Y equals sine X by 20 units to the right B says to translate the graph of Y equals sine X by 20 units upward. C says to stretch the graph vertically by a factor of 20 D says to compress the graph of Y, you call sin X the same graph vertically by a factor of 20. Now, what are we trying to do here? Well, basically we're taking the graph of Y equals sin X. OK. And we're trying to figure out what our equation will tell us to do to this graph. OK. Because this equation is just a transformation of our basic sine graph. So what do we know about the sine function that can help us? Well, recall, right, recall that every sine function is written in a form Y equals a multiplied by the sine of BX minus C plus D. OK. Where A is A, helps us to find our amplitude A is our amplitude. OK. And if A is greater than one, that means our graph is going to stretch. But if it's less than one, that means it's going to compress. So if we can look at our equation because I don't, we, we don't necessarily need to go any further because that's what we're concerned with, right? Because the only difference between both is the 20 that's being multiplied by sine X. So if we can look at our graph and figure out what that 20 means, then we should be able to tell what happens. So let's compare our equation. We know that our equation because Y equals 20 sine X. OK. So what's the difference between both of these? Well, here notice that this tells us that 20 is our amplitude. OK. So that means A equals 20 and since a equals 20 that represents the amplitude, that means our graph is going to stretch the graph of Y equals sine X vertically by a factor of 20. When we look back on our answer choices, that would have been answer choice. C Thanks a lot for watching everyone. I hope this video helps.

Fill in the blank(s) to correctly complete each sentence.
The graph of y = 4 sin x is obtained by stretching the graph of y = sin x vertically by a factor of ________.

Key Concepts

Vertical Stretch

Amplitude

Transformation of Functions

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