Will mark brainliest and give 20 points! In what ways can vertical, horizontal, and oblique asymptotes be identified? Please use your own example to identify.
Question
Answer:
Think of asy. as limiting fences to where your graph can travel. If, for example, you graph y = 1/x properly, you'll see that the graph never crosses either the x- or the y-axis. As x increases, your graph will get closer and closer to the line y=0 (which happens to be the horiz. axis), but will not cross it. Similarly, as x approaches x=0, the graph gets closer and closer to the vert. axis, x=0, but will not cross it. Do you see how the asymptotes limit where the graph can go?Vertical asy. stem only from rational functions and correspond to x-values for which the denominator = 0. As you know, we can NOT divide by zero. Instead, we draw a vertical line thru any x-value at which the rational function is not defined.Horiz. asy. have to do with the behavior of functions as x grows increasingly large, whether pos. or neg. Go back and re-read my earlier comments on horiz. asy. As x grows incr. large, in the positive direction, the graph of y=1/x approaches, but does not touch or cross, the horiz. asy.I will stop here and encourage you to ask questions if any of this discussion is not clear.
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