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brandon26
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Could anyone show me what the graph of y=(x+1)/(x-1) looks like?
The graph for y=(x+1)/(x-1) is a hyperbola, which is a type of curve with two branches that open in opposite directions. It is symmetrical about the line x=1 and x=-1.
The x-intercept is the point where the graph crosses the x-axis, and the y-intercept is the point where the graph crosses the y-axis. For y=(x+1)/(x-1), the x-intercept is (1,0) and the y-intercept is (0,-1).
Yes, there are two asymptotes in the graph for y=(x+1)/(x-1): a vertical asymptote at x=1 and a horizontal asymptote at y=1. These asymptotes occur because the function is undefined at x=1 and approaches infinity as x approaches 1, and the function approaches 1 as x approaches infinity.
The domain of y=(x+1)/(x-1) is all real numbers except x=1, since the function is undefined at that point. The range is also all real numbers except y=1, since the function approaches that value but never reaches it.
Changing the value of x will shift the graph horizontally and vertically. For example, if x is increased, the graph will shift to the left, and if x is decreased, the graph will shift to the right. Additionally, the graph will approach the asymptotes as x approaches 1.