Graph y=1/x

Problem

y=1/x

Solution

1. Identify the function type and its domain. This is a reciprocal function, which is a type of rational function. The domain is all real numbers except x=0 where the function is undefined.

2. Determine the asymptotes of the graph. As x approaches 0 y approaches infinity or negative infinity, resulting in a vertical asymptote at x=0 As x becomes very large or very small, y approaches 0 resulting in a horizontal asymptote at y=0

3. Find key points to plot in each quadrant. For x>0 points include (1,1) (2,0.5) and (0.5,2) For x<0 points include (−1,−1) (−2,−0.5) and (−0.5,−2)

4. Sketch the curves in the first and third quadrants. The graph consists of two separate branches (a hyperbola) that approach the axes but never touch them.

Final Answer

y=1/x

The graph is a hyperbola with a vertical asymptote at x=0 and a horizontal asymptote at y=0 passing through points such as (1,1) and (−1,−1)

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