Graph y=2/x

Problem

y=2/x

Solution

1. Identify the function type as a rational function or hyperbola, which has a vertical asymptote where the denominator is zero.

2. Determine the asymptotes by setting the denominator to zero for the vertical asymptote x=0 and observing the limit as x approaches infinity for the horizontal asymptote y=0

3. Find key points by substituting values for x to determine the shape of the curve in different quadrants.

4. Calculate points for x>0 such as (1,2) (2,1) and (4,0.5) which shows the graph is in the first quadrant.

5. Calculate points for x<0 such as (−1,−2) (−2,−1) and (−4,−0.5) which shows the graph is in the third quadrant.

6. Sketch the curves by drawing two smooth branches that approach the axes but never touch them.

Final Answer

y=2/x

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