Determine an equation for each graph.

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Accepted Answer

Hello, today we are going to be writing an equation that represents the graph of the trigonometric function shown below. So we are given the graph of an unknown trigonometric function. But there are two important pieces of information that are given to us that tell us what function we are working with. The graph shows us that we have vertical asymptotes located at negative pi divided by two and positive pi divided by two. What this tells us is that we are working with the seek and function. So let's go ahead and graph the standard form of the seek and function. The second function has two vertical asymptotes. They are located at negative pi divided by two and positive pi divided by two. Another thing to note is that there is a horizontal Asymptote of Y is equal to zero for the sequin function. The maximum value for the seek and function is located at zero comma one and the minimum values of the seek and function are located at negative pi comma negative one and positive pi comma negative one. For the maximum value, all the values of seeking will increase to positive infinity when approaching negative pi divided by two and positive pi divided by two. And at the minimum values, the graph will approach negative infinity as it approaches negative pi divided by two and positive pi divided by two. So this is the standard graph for the sin function. Let's go ahead and identify the horizontal Asymptote of the given graph. Now looking at the positive and at the minimum and maximum values, the minimum and maximum values are exactly two units away from each other. What this means is that we have a horizontal Asymptote at Y is equal to negative four. What this means is that there has to be a vertical shift of four units down for the seek and function. What this means is that we are going to be subtracting four to the seek and function. Furthermore, if we take a look at the given shape and compare to our traditional function, it appears that the function is rotated about the horizontal Asymptote. Since we are rotating about the horizontal Asymptote, the seeking function must have a negative leading coefficient. And if we reorder the terms, we can rewrite the function as negative four minus seeking of X. This is going to be the equation that represents the unknown trigonometric function. And with that being said, the answer to this problem is going to be D. So I hope this video helps you in understanding how to approach this problem. And I'll go ahead and see you all in the next video.

Determine an equation for each graph.

Key Concepts

Graphing Trigonometric Functions

Amplitude and Period

Phase Shift

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