# What is the range of the function y = x?

Sep 24, 2014

The range of a function is all possible output, or $y$, values. The domain is all possible input, or $x$, values. In the case of $y = x$, both the range and domain are all real numbers.You can plug in all sorts of negative and positive $x$ and $y$ values; there are no restrictions. So, in interval notation

The range: (-∞, ∞)
The domain: (-∞, ∞)

Note the round brackets ( ) because since infinity isn't a number, the functions can't be defined there. The functions just tend to infinity as the $x$ and $y$ values get infinitely large or infinitely small.

The function $y = x$ is an interesting case of domain and range because the domain and range values are always the same. In other words, since $y$ always equals $x$, the input values always equal the output values.$y = x$ is also actually just the graph of a straight line, with a slope of 1 and a $y$-intercept at (0,0). You'll see that all points will have equivalent values, so some points on the line would be (4,4) or (-178, -178). To graphically observe the equivalence of the domain and range, here is a graph of the line: 