Question Video: Graphing Trigonometric Functions Mathematics • 10th Grade

Which of the following is the graph of 𝑦 = −tan (𝑥)? [A] Graph A [B] Graph B [C] Graph C [D] Graph D [E] Graph E

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Video Transcript

Which of the following is the graph of 𝑦 equals negative tan of 𝑥?

Let’s just begin by recalling what the graph of 𝑦 equals tan of 𝑥 looks like. It’s periodic, and it repeats every 180 degrees. It passes through the origin, the point zero, zero. It has vertical asymptote at 𝑥 equals 90 degrees but also every 180 degrees either side of this, in other words, 𝑥 equals negative 90, 𝑥 equals 270, and so on. In fact, the graph of 𝑦 equals tan of 𝑥 is this one. It’s (A).

Notice that the graph approaches the asymptotes but never actually quite touches them. But of course, we were interested in the graph of 𝑦 equals negative tan of 𝑥. So, we recall that for a function 𝑦 equals 𝑓 of 𝑥, 𝑦 equals negative 𝑓 of 𝑥 is a reflection in the 𝑥-axis. And we see that the only graph that matches this is (D). (D) is the graph of 𝑦 equals negative tan of 𝑥.

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