The
problem is about graphing a rational function. This video addresses vertical, horizontal, and slant asymptotes, and finds the holes and the x and y-intercepts of the function. Using
past concepts (domain, long division, interval notation) will
help us in graphing this function.
We need to pay special attention how to find the x and y-intercepts because it is crucial to remember to use the simplified equation, not the original rational function. Another concept we need to pay attention to finding the holes, plugging in the found x-value into the simplified equation to find the y-value of the hole. When plotting the hole, represent it as an open circle, which symbolizes that the graph does not go through this point. Lastly, through using the limit notation of the vertical asymptote, it gives you an idea of what the graph will look like.
We need to pay special attention how to find the x and y-intercepts because it is crucial to remember to use the simplified equation, not the original rational function. Another concept we need to pay attention to finding the holes, plugging in the found x-value into the simplified equation to find the y-value of the hole. When plotting the hole, represent it as an open circle, which symbolizes that the graph does not go through this point. Lastly, through using the limit notation of the vertical asymptote, it gives you an idea of what the graph will look like.
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