Graph 1/(x^2)

Problem

ƒ(x)=1/(x2)

Solution

1. Identify the domain and vertical asymptotes by finding where the denominator is zero. Since x2=0 when x=0 there is a vertical asymptote at x=0

2. Determine the horizontal asymptote by observing the behavior as x approaches infinity. As x→∞ or x→−∞ ƒ(x)→0 so the horizontal asymptote is y=0

3. Check for symmetry by evaluating ƒ*(−x) Since ƒ*(−x)=1/((−x)2)=1/(x2)=ƒ(x) the function is even and symmetric about the yaxis.

4. Analyze the range by noting that x2 is always positive for all x≠0 Therefore, ƒ(x)>0 for all x in the domain, meaning the graph stays above the xaxis.

5. Plot key points to determine the shape. For x=1 y=1 For x=2 y=1/4 For x=1/2 y=4 Use symmetry to mirror these points across the yaxis.

Final Answer

ƒ(x)=1/(x2)

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