In Exercises 1–4, the graph of a tangent function is given. Selec...

Question

In Exercises 1–4, the graph of a tangent function is given. Select the equation for each graph from the following options: y = tan(x + π/2), y = tan(x + π), y = −tan(x − π/2).

Graph of the tangent function with vertical asymptotes and key points labeled.

Accepted Answer

Hello, today we're gonna be identifying the equation of the given graph. Now, one thing to note is that the graph is in the rough shape of a tangent graph. So in order to identify the equation for the tangent graph, let's take a look at the parent function tangent of X. The pair function of tangent of X has an X intercept at the origin zero comma zero. The period for tangent of X is going to be pi and tangent of X has asymptotes located at positive pi over two, a negative pie over two. And the shape of the tangent graph is going to roughly look like this. So let's use the pair function and compare the given graph to identify the equation. The first thing that we can see is that the shape of the graph is flipped along the X axis. What this means is that the current, the current transformation can be labeled as Y is equal to negative tangent of X since the graph has been reflected about the X axis. Another thing to note is that the X intercept given to us is pi over three. Now note that for the first rotation or for the first period of tangent, the X intercept is at the origin. So what this means is that the X intercept would have shifted pi over three units to the right. That means we have a horizontal shift for the graft of pi over three units to the right. And what this means is that we can represent a horizontal shift using X minus H. In this case, here, H is going to equal to pi over three. So that means that we can represent the horizontal shift as X minus pi over three. These are the only two transformations that occur for the given graph. So if we combine these two transformations, the equation of the graph is going to be Y is equal to negative tangent of X minus pi over three. And with that being said, the answer to this problem is going to be D. So I hope this video helps you in understanding how to approach this problem. And I'll go ahead and see you all in the next video.

In Exercises 1–4, the graph of a tangent function is given. Select the equation for each graph from the following options: y = tan(x + π/2), y = tan(x + π), y = −tan(x − π/2).

Key Concepts

Tangent Function Properties

Phase Shift

Vertical Asymptotes

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