What is the domain and range of the graph f(x)=1/x?

Jun 6, 2018

Both the domain and range are: all real numbers except for zero.

Explanation:

Domain is all the possible x-values that can be plugged in and range is all the possible y-values that can be outputs.

$f \left(x\right) = \frac{1}{x}$ can have any number as an input except for zero.

If we plug in zero for $x$, then we would be dividing by zero which is impossible.

Thus the domain is all real numbers except for zero.

The range is easier to see on the graph:

graph{1/x [-10, 10, -5, 5]}

Since the function goes up forever and down forever vertically, we can say that the range too is all real numbers except for zero.