Question Video: Transforming Graphs with Arithmetic Operations | Nagwa Question Video: Transforming Graphs with Arithmetic Operations | Nagwa

# Question Video: Transforming Graphs with Arithmetic Operations

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

01:24

### 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 over two, ๐, three ๐ over two, and two ๐, so we have to plug in values in these ๐s. So letโs plug in ๐ over two. And the sin of ๐ over two is one, so if we plug this into our function, and the sin of ๐ over two is one; one divided by one is one, so at ๐ over two, we should be at one.

In our yellow graph, when weโre at ๐ over two, we get zero for ๐ฆ, so that doesnโt work, but in our red graph, at ๐ over two, weโre at about one. Therefore, this red graph will be the graph of our function.

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