DensityPlot
[f, {x, $x_{min}$, $x_{max}$}, {y, $y_{min}$, $y_{max}$}]DensityPlot[x ^ 2 + 1 / y, {x, -1, 1}, {y, 1, 4}]
DensityPlot[1 / x, {x, 0, 1}, {y, 0, 1}]
DensityPlot[Sqrt[x * y], {x, -1, 1}, {y, -1, 1}]
DensityPlot[1/(x^2 + y^2 + 1), {x, -1, 1}, {y, -2,2}, Mesh->Full]
DensityPlot[x^2 y, {x, -1, 1}, {y, -1, 1}, Mesh->All]