Identify any vertical, horizontal, or oblique asymptotes in th...

Question

Identify any vertical, horizontal, or oblique asymptotes in the graph of $y=f\left(x\right)$ . State the domain of $f$ .

Accepted Answer

Hello. In this video, we are going to be determining the asymptotes of the given graph and also identifying its domain. So let's go ahead and start by first identifying the vertical Asymptote. Now, the vertical Asymptote causes the graph to have a sort of volcano shape or pit shape. And if we are taking a look at the given graph notice that the graph has a volcano shape at the value X is equal to four. What this means is that the graph is going to continuously approach the value of four but never actually equal to four, meaning that four is acting as a restriction on the graph. This means that the vertical Asymptote is going to exist when X is equal to four. Next, let's go ahead and identify the horizontal Asymptote. Now, the horizontal Asymptote is a value of Y that the graph tends to stay right next to above or below. And if we are taking a look at this given graph notice that the graph is consistently above the value at Y is equal to two, that means that the graph is going to continuously approach the value Y is equal to two. But never actually cross that value. And that means that the graph or the equation of the line Y is equal to two is going to act as the horizontal Asymptote to the given to the given graph. Now, what about its domain? While the domain of the graph includes all the values except for the vertical asymptotes. Since the vertical Asymptote is located at positive four, that means the domain of the graph is going to be all real numbers, not including four or in set builder notation will be from negative infinity to positive four, not including the value union positive four to positive infinity. So by just looking at the graph, we determine that the vertical Asymptote is going to be positive four. The horizontal Asymptote is Y is equal to two and the domain is going to be all real numbers not including the value of four. With that being said, the solution to this problem is going to be C So I hope this video helps you in understanding how to site read a graph. And I'll go ahead and see you all in the next video.

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Identify any vertical, horizontal, or oblique asymptotes in the graph of $y=f\left(x\right)$ . State the domain of $f$ .
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