Reciprocal Function
f(x) = 1 / x
A reciprocal function is a type of function in mathematics which takes the form f(x) = 1/x, where x is the independent variable, and f(x) is the dependent variable. In other words, the value of the function is the reciprocal (1 divided by) of the input value.
The graph of a reciprocal function is a hyperbola, which is a shape that looks like two curved lines that move away from each other to infinity. The vertical asymptote is the line where the function is undefined, which in this case is the line x = 0 (the y-axis). The horizontal asymptote is the line towards which the curve approaches as x becomes very large or very small, which in this case is the line y = 0 (the x-axis).
Reciprocal functions are used in many applications, such as in physics, engineering and economics. In physics, they are used to describe inverse relationships between variables, such as the relationship between distance and time. In economics, they are used to model the relationship between quantity and price in demand and supply curves.
It is important to note that reciprocal functions are not defined at x = 0, as this would result in a division by zero error. It is also important to be aware of the behavior of the function close to the asymptotes, where the function can become very large or very small very quickly.
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