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

Question

The graph of y = -3 sin x is obtained by stretching the graph of y = sin x by a factor of ________ and reflecting across the ________-axis.

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 negative 12 sine X from the graph of Y equals sine X. It says that we're going to stretch the graph of Y equals sine X vertically by a factor of 12 and reflect it across the Y axis B says we're going to stretch the graph vertically by a factor of 12 and reflect it across the X axis C says we will compress the graph and compress the graph vertically by a factor of 12 and reflected across the X axis. And this says we will translate the graph by 12 units to the left. Now, let's try to understand what we're really thinking here. So essentially what we're seeing is that our graph of Y equals sine X can basically be transformed to show the graph that we have here without plotting the points. In other words, this graph Y equals negative 12 sine X is just a transformation of sin X. And we want to figure out what transformation that is going to be. Now, what do we know about a graph uh or, or, or a trigonometric graph. Well, recall and recall that for any graph, any trigonometric graph Y equals a multiplied by F of X, then it's either a vertical search or vertical compression of the graph Y equals F of X by a factor of the magnitude of A. OK. We know as well that if A is negative. In other words, if A is less than zero, then our graph is going to be vertically stretched or compressed and reflected across the X axis. So in other words, our result would look something like this. OK? And we also know that if the magnitude of A is greater than one, OK. If the magnitude of A is, let's write that here, the magnitude of A is greater than one, whether positive or negative, its magnitude just has to be greater than one, then it's going to be a stretch. Well, if its magnitude is less than one, OK, then we know that it's going to be a compression. So those are the things we know about our Vertica stretch. So we need to first compare our equation to the general form. And once we identify A, then we'll use the information here to help us figure out what happens to our graph. So given our phone that said Y equals negative 12 sine X, OK. If we compare the general form to our function, what do you notice? Well, you'll notice here that A equals negative 12. OK. Now, for our number notice that A is less than zero A is negative. So that means there's going to be a reflection in the X axis. Also notice that the magnitude of A equals 12 and 12 is greater than one. So since its magnitude is greater than one, it's going to be a stretch. Therefore, or graph to the graph of Y equals negative 12 sine X can be obtained by vertically stretching. The graph of Y equals sine X by a factor of 12 and reflecting it across the X axis since it's negative. If we look back in our answer, choices that would have been answer choice B 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 = -3 sin x is obtained by stretching the graph of y = sin x by a factor of and reflecting across the -axis.

Key Concepts

Amplitude and Vertical Stretch

Reflection Across Axes

Graphing Transformations

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