Q:

Area-colored phase diagram for various ranges of f(a,b), given the ranges of a and b

Is there a way to plot a simple diagram in Mathematica with colored areas, like a phase diagram, for the different ranges of values of a function such $f(a,b)=(1-a)/(b+2)$, for various combinations of $a$ & $b$? 
I mean, for example, if $0<a<1$ and $0<b<2$, plot a diagram where the x-axis is $a$, and the y-axis is $b$, in which the area where $1/4<f<1/2$ is colored red, and $0<f<1/4$ is colored blue and the rest is white?  

A:

Try RegionPlot(I changed your example a little bit because of 0<f<1/2)
Show[{
RegionPlot[0 < (1 - a)/(2 + b) < 1/4, {a, 0, 1}, {b, 0, 2},PlotStyle -> Blue],
RegionPlot[1/4 < (1 - a)/(2 + b) < 1/2, {a, 0, 1}, {b, 0, 2},PlotStyle -> Red]
}]

