Question Video: Graphing Trigonometric Functions Mathematics • 10th Grade

Which of the following is the graph of ๐‘ฆ = โˆ’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.

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