Graph 1/x

Problem

ƒ(x)=1/x

Solution

1. Identify the domain by finding values where the denominator is zero. Since x≠0 the domain is (−∞,0)∪(0,∞)

2. Determine the asymptotes of the function. There is a vertical asymptote at x=0 and a horizontal asymptote at y=0 because (lim_x→±∞)(1/x)=0

3. Analyze the behavior in different quadrants. For x>0 the function is positive and decreasing. For x<0 the function is negative and increasing.

4. Plot key points to define the shape of the hyperbola. For example, (1,1) (2,0.5) (−1,−1) and (−2,−0.5)

5. Sketch the curves in the first and third quadrants, ensuring they approach the asymptotes without touching them.

Final Answer

ƒ(x)=1/x

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