Graph F(x)=1/x

Problem

F(x)=1/x

Solution

1. Identify the function type: The function F(x)=1/x is a reciprocal function, which is a type of rational function that forms a hyperbola.

2. Determine the domain: Since the denominator cannot be zero, x≠0 The domain is (−∞,0)∪(0,∞)

3. Identify asymptotes: As x approaches 0 F(x) approaches ±∞ indicating a vertical asymptote at x=0 As x approaches ±∞ F(x) approaches 0 indicating a horizontal asymptote at y=0

4. Analyze symmetry: Since F*(−x)=1/(−x)=−F(x) the function is odd, meaning the graph is symmetric with respect to the origin.

5. Plot key points: Calculate coordinates for several values of x to determine the shape.

F(1)=1

F(2)=0.5

F(0.5)=2

F*(−1)=−1

F*(−2)=−0.5

F*(−0.5)=−2

6. Sketch the curves: Draw two smooth curves (branches) in the first and third quadrants that approach the axes but never touch them.

Final Answer

F(x)=1/x

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