Question Video: Transforming Graphs with Arithmetic Operations Mathematics

Which of the following is the graph of the function ๐‘“(๐‘ฅ) = 1/sin(๐‘ฅ)?

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Video Transcript

Which of the following is the graph of the function ๐‘“ of ๐‘ฅ equals one divided by the sin of ๐‘ฅ?

Letโ€™s first plug in some values that we know for the sin of ๐‘ฅ. The sin of zero is zero. So if we would take our function and plug in zero for ๐‘ฅ of sin of zero, we know thatโ€™s zero, but one divided by zero, actually anything divided by zero is undefined, so it canโ€™t actually work.

So in these two top graphs, itโ€™s showing values at zero. So when ๐‘ฅ is zero in the blue graph, weโ€™re at around one, and then in the green graph, at zero, weโ€™re at zero. So we can eliminate these.

Something else we can plug in now notice weโ€™re plugging in for ๐‘ฅ, and our ๐‘ฅ values are zero, ๐œ‹ over two, ๐œ‹, three ๐œ‹ over two, and two ๐œ‹, so we have to plug in values in these ๐œ‹s. So letโ€™s plug in ๐œ‹ over two. And the sin of ๐œ‹ over two is one, so if we plug this into our function, and the sin of ๐œ‹ over two is one; one divided by one is one, so at ๐œ‹ over two, we should be at one.

In our yellow graph, when weโ€™re at ๐œ‹ over two, we get zero for ๐‘ฆ, so that doesnโ€™t work, but in our red graph, at ๐œ‹ over two, weโ€™re at about one. Therefore, this red graph will be the graph of our function.

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