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vertical asymptote x=3, y=-(3)/(5(x-3)^(2)) vertical asymptote x=-2, y=(2)/(5(x+2)) horizontal asymptote y=-2 x=0, y=-(x)/(6)

User Sumitya
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Final answer:

The question pertains to the understanding of vertical and horizontal asymptotes in rational functions, which define the behavior of the graph of the function as x approaches certain values or infinity.

Step-by-step explanation:

The student's question revolves around the concepts of asymptotes and rational functions in mathematics, particularly dealing with vertical asymptotes, horizontal asymptotes, and how they are represented in equations. A vertical asymptote is where the function approaches infinity as x approaches a certain value. For instance, when the student mentions x=3, it means as x approaches 3, the function y=-(3)/(5(x-3)^(2)) goes to infinity, describing a vertical asymptote. Similarly, for x=-2 and y=(2)/(5(x+2)), x approaching -2 reflects another vertical asymptote. A horizontal asymptote, like y=-2, suggests that as x approaches infinity, the y-value of the function will approach -2. Understanding both vertical and horizontal asymptotes is crucial for graphing these rational functions and understanding their behavior at different values of x.

User Akf
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