The reciprocal function is a function that pairs each x-value with its reciprocal.
x | f(x) |
1 | 1 |
2 | 21 |
3 | 31 |
4 | 41 |
⋮ | ⋮ |
The function rule of the reciprocal function is obtained algebraically by writing the rule for the pairings shown in the table above.
f(x)=x1,x=0
The domain and range are all nonzero real numbers. Its graph is a hyperbola, which consists of two symmetrical parts called branches. Furthermore, it has two asymptotes: the x- and y-axis.
The reciprocal function is a member of a larger family of functions used to model inverse variations. These functions have the general form xk, where both the constant k and the x-variable are nonzero. For this reason, the reciprocal function is also known as the inverse variation parent function.
It is important not to confuse the reciprocal of a function with the inverse of a function. For numbers, a-1 refers to the reciprocal a1, while the notation f -1(x) is commonly used to refer to the inverse of a function.
Function, f | Reciprocal, f1 | Inverse, f-1 |
---|---|---|
f(x)=2x+10 | f(x)1=2x+101 | f -1(x)=21(x−10) |
f(x)=x3−5 | f(x)1=x3−51 | f -1(x)=3x+5 |