# Question Video: Graphing Trigonometric Functions Mathematics • 10th Grade

Which of the following is the graph of ๐ฆ = โtan (๐ฅ)? [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 ๐ฆ equals negative tan of ๐ฅ?

Letโs just begin by recalling what the graph of ๐ฆ equals tan of ๐ฅ looks like. Itโs periodic, and it repeats every 180 degrees. It passes through the origin, the point zero, zero. It has vertical asymptote at ๐ฅ equals 90 degrees but also every 180 degrees either side of this, in other words, ๐ฅ equals negative 90, ๐ฅ equals 270, and so on. In fact, the graph of ๐ฆ equals tan of ๐ฅ is this one. Itโ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 ๐ฆ equals negative tan of ๐ฅ. So, we recall that for a function ๐ฆ equals ๐ of ๐ฅ, ๐ฆ equals negative ๐ of ๐ฅ is a reflection in the ๐ฅ-axis. And we see that the only graph that matches this is (D). (D) is the graph of ๐ฆ equals negative tan of ๐ฅ.