k11 = 1;
k12 = 0.1;
k21 = 1;
k22 = 10;
rate1 = k11*cA/(1 + k12*cA);
rate2 = k21*cA/(1 + k22*cA);
Plot[{rate1, rate2}, {cA, 0, 1}, AxesOrigin -> {0, 0}, 
        PlotRange -> {0, 0.1}, 
        PlotStyle -> {Thickness[0.005], 
            Thickness[0.008]}];

Here you see clearly that when k22*cA>>1 (at high cA), the reaction tends to be zero order (thick line) while, when k12*cA<<1 (at low cA), the reaction is first order (thin line).
For any reaction whose rate has the same kinetic expression (the so called Langmuir-Hinshelwood or Michaelis-Menten rate equation), regardless of the values of the rate constants, there is a low-concentration region where the rate is 1st order and a high-concentration region where the rate is zero order. See for yourself, by using different concentration ranges below (e.g., 0 to 20 vs. 0 to 0.2).

k1 = 1;
k2 = 1;
rateNew = k1*cA/(1 + k2*cA);
Plot[rateNew, {cA, 0, 0.2}];