ATTENTION: There was a slight mistake in my answer for the hole, but the correct hole for the equation above, is this one! Sorry for the inconvenience.
Here is the graph I promised in the video! A quick explanation of the graph the highlighted parts: the green in the vertical asymptote and the blue is the slant asymptote. The points on the graph are the x-intercepts and y-intercepts found throughout the equation. And lastly the key points are points randomly selected. The process is you choose three x-values that are on the graph and on your graphing calculator, looking at your graph, you trace those three x's and you shall receieve your y's.
What is this problem about?
The problem is about basically everything to do with rational functions! I know very exciting. But anyways in a problem like this we will see horizontal asymptotes/slant asymptotes, vertical asymptotes, holes, domain, x-intercepts, y-intercepts and in the end adding everything into one bunch and graphing it. Everything interconnects with one another, so it is important to be clear with your work so in the end you won't mess up the graph.
What does the viewer need to pay special attention in order to understand?
In order to understand the viewer must pay attention to each and every step they do. They must be aware that one thing leads to another and it all leads to the graph. So it must be important to keep everything organized because you can easily mess one thing up with another. It's extremely important to REMEMBER that if you have a slant asymptote you will not be having a horizontal asymptote and vice versa. Laslty, if nothing cancels in a vertical asymptote that means the graph will not have a hole.
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