real analysis - graph is dense in $mathbb{R}^2$

I was asked in a exam: does there exist a function(need not be continous) $f:\mathbb{R}\rightarrow \mathbb{R}$ whose graph is dense in $\mathbb{R}^2$?

I proved that graph of a discontinuous linear map is dense but did not provide explicit example, could any one give me one such? thank you