### Video Transcript

Which of the following is the graph
of π¦ equals negative tan of π₯?

Letβs just begin by recalling what
the graph of π¦ equals tan of π₯ looks like. Itβs 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. Itβs (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₯.