Question Video: Graphing Trigonometric Functions Mathematics

Which of the following is the graph of 𝑦 = βˆ’tan (π‘₯)? [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 π‘₯?

Let’s just begin by recalling what the graph of 𝑦 equals tan of π‘₯ 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 π‘₯ equals 90 degrees but also every 180 degrees either side of this, in other words, π‘₯ equals negative 90, π‘₯ equals 270, and so on. In fact, the graph of 𝑦 equals tan of π‘₯ 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 π‘₯. So, we recall that for a function 𝑦 equals 𝑓 of π‘₯, 𝑦 equals negative 𝑓 of π‘₯ is a reflection in the π‘₯-axis. And we see that the only graph that matches this is (D). (D) is the graph of 𝑦 equals negative tan of π‘₯.

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