Question

How do you find the domain and range of `f(x)=x`?

Answer 1

The domain of `f(x) = x` is the whole of the real numbers `RR`. The range is also the whole of `RR`.

Explanation:

Given:

`f(x) = x`

• The domain of `f(x)` is the set of values for which `f(x)` is defined. In the context of Algebra I that means a subset of the real numbers `RR`. In the case of the given `f(x)`, it is well defined for any `x in RR`, so the domain is the whole of `RR`, i.e. `(-oo, oo)`

• The range of `f(x)` is the set of values that it can take for some value of `x`. Given any real number `y`, let `x = y`. Then `f(x) = x = y`. So the range of `f(x)` is the whole of `RR` too.

The graph of `f(x) = x` is a diagonal line like this:

# graph{x [-10, 10, -5, 5]}

For every `x` coordinate there is a corresponding point on the line. That tells us that the domain of `f(x)` is the whole of `RR`.

For every `y` coordinate there is a corresponding point on the line. That tells us that the range of `f(x)` is the whole of `RR`.