Graph of y = 1/x
Interactive graph of y = 1/x (reciprocal function). Explore the hyperbola, its asymptotes, and odd symmetry with our free graphing calculator.
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Understanding the Function
The reciprocal function y = 1/x produces a hyperbola with two branches: one in the first quadrant (where both x and y are positive) and one in the third quadrant (where both are negative). The function is undefined at x = 0 and approaches zero as x approaches positive or negative infinity.
This function has two asymptotes: a vertical asymptote at x = 0 (the y-axis) and a horizontal asymptote at y = 0 (the x-axis). It is an odd function with rotational symmetry about the origin, and it is its own inverse (applying 1/x twice returns to x).
Key properties: domain is all real numbers except 0, range is all real numbers except 0, no intercepts, derivative is -1/x². The function represents inverse proportionality and appears in physics (Coulomb's law, gravitational fields), economics (supply-demand curves), and optics (lens equations).