# Question Video: Graphing Trigonometric Functions Mathematics

Which of the following is the graph of π¦ = β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 π¦ equals negative tan of π₯?

Letβs just begin by recalling what the graph of π¦ equals tan of π₯ looks like. Itβ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 π¦ equals tan of π₯ is this one. Itβ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 π¦ equals negative tan of π₯. So, we recall that for a function π¦ equals π of π₯, π¦ equals negative π 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 π¦ equals negative tan of π₯.