Which of the following is the graph
of 𝑦 equals negative tan of 𝑥?
Let’s just begin by recalling what
the graph of 𝑦 equals tan of 𝑥 looks like. It’s periodic, and it repeats every
180 degrees. It passes through the origin, the
point zero, zero. It has vertical asymptote at 𝑥
equals 90 degrees but also every 180 degrees either side of this, in other words, 𝑥
equals negative 90, 𝑥 equals 270, and so on. In fact, the graph of 𝑦 equals tan
of 𝑥 is this one. It’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 𝑦 equals negative tan of 𝑥. So, we recall that for a function
𝑦 equals 𝑓 of 𝑥, 𝑦 equals negative 𝑓 of 𝑥 is a reflection in the 𝑥-axis. And we see that the only graph that
matches this is (D). (D) is the graph of 𝑦 equals
negative tan of 𝑥.