WEBVTT
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Which of the following is the graph of π¦ equals negative tan of π₯?
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Letβs just begin by recalling what the graph of π¦ equals tan of π₯ looks like.
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Itβs periodic, and it repeats every 180 degrees.
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It passes through the origin, the point zero, zero.
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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.
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In fact, the graph of π¦ equals tan of π₯ is this one.
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Itβs (A).
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Notice that the graph approaches the asymptotes but never actually quite touches them.
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But of course, we were interested in the graph of π¦ equals negative tan of π₯.
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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.
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And we see that the only graph that matches this is (D).
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(D) is the graph of π¦ equals negative tan of π₯.