Which of the following is the graph of the function 𝑓 of 𝑥 equals one divided by the sin of 𝑥?
Let’s first plug in some values that we know for the sin of 𝑥. The sin of zero is zero. So if we would take our function and plug in zero for 𝑥 of sin of zero, we know that’s zero, but one divided by zero, actually anything divided by zero is undefined, so it can’t actually work.
So in these two top graphs, it’s showing values at zero. So when 𝑥 is zero in the blue graph, we’re at around one, and then in the green graph, at zero, we’re at zero. So we can eliminate these.
Something else we can plug in now notice we’re plugging in for 𝑥, and our 𝑥 values are zero, 𝜋 over two, 𝜋, three 𝜋 over two, and two 𝜋, so we have to plug in values in these 𝜋s. So let’s plug in 𝜋 over two. And the sin of 𝜋 over two is one, so if we plug this into our function, and the sin of 𝜋 over two is one; one divided by one is one, so at 𝜋 over two, we should be at one.
In our yellow graph, when we’re at 𝜋 over two, we get zero for 𝑦, so that doesn’t work, but in our red graph, at 𝜋 over two, we’re at about one. Therefore, this red graph will be the graph of our function.