Graph f(x)=1/(x^2)

Problem

ƒ(x)=1/(x2)

Solution

1. Identify the domain and check for vertical asymptotes. Since the denominator is zero when x=0 the function is undefined at x=0 resulting in a vertical asymptote at x=0

2. Determine the horizontal asymptote by examining the limit as x approaches infinity. As x→∞ or x→−∞ ƒ(x)→0 so there is a horizontal asymptote at 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 and behavior. Because x2 is always positive for all x≠0 ƒ(x) is always positive, meaning the graph stays entirely above the xaxis.

5. Plot key points to define the shape. For x=1 ƒ(1)=1 For x=2 ƒ(2)=1/4 For x=1/2 ƒ(1/2)=4 Use symmetry to mirror these points across the yaxis.

Final Answer

ƒ(x)=1/(x2)

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