# Thread: Do all linear functions have a natural domain/range of all real numbers?

1. ## Do all linear functions have a natural domain/range of all real numbers?

Do all linear functions have a natural domain of all real numbers?

Do all linear functions have a range of all real numbers?

Explain, because I'm still a bit muddled on the topic and don't know how to write it all out!

Much thanks!

2. ## Re: Do all linear functions have a natural domain/range of all real numbers?

Domain of a linear function is all reals, however, not all linear functions have a range of all reals ... consider the linear function $y = k$ where $k$ is a constant.

3. ## Re: Do all linear functions have a natural domain/range of all real numbers?

Hey ellenoel.

What do you define for linear functions?

Do you use y = ax + b or do you use the f(x+y) = f(x) + f(y) and f(ax) = a*f(x)?

4. ## Re: Do all linear functions have a natural domain/range of all real numbers?

The domain of a linear function in the form of y=mx+b have a domain of x=all real numbers, and a range of y=all real numbers, unless the slope (m) of the line equals zero. In that case it becomes y=b, where all values of x will have the same y value or range. The line of a constant. I hope this helps. ��