Question

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

Answer 1

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(x)=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.