Video Transcript
Which of the following is the graph
of ๐ฆ equals negative tan of ๐ฅ?
Letโs just begin by recalling what
the graph of ๐ฆ equals tan of ๐ฅ looks like. Itโs periodic, and it repeats every
180 degrees. It passes through the origin, the
point zero, zero. It has vertical asymptote at ๐ฅ
equals 90 degrees but also every 180 degrees either side of this, in other words, ๐ฅ
equals negative 90, ๐ฅ equals 270, and so on. In fact, the graph of ๐ฆ equals tan
of ๐ฅ is this one. Itโs (A).
Notice that the graph approaches
the asymptotes but never actually quite touches them. But of course, we were interested
in the graph of ๐ฆ equals negative tan of ๐ฅ. So, we recall that for a function
๐ฆ equals ๐ of ๐ฅ, ๐ฆ equals negative ๐ of ๐ฅ is a reflection in the ๐ฅ-axis. And we see that the only graph that
matches this is (D). (D) is the graph of ๐ฆ equals
negative tan of ๐ฅ.
