I began to prepare this answer with some hesitation. Looking at the attractive (and interactive) colorful Falstad simulation and detailed explanations in the subtleties of an indisputably great professional, I wondered, "Is it possible to counteract all this with a simple human explanation based on intuition and common sense... and illustrated with hand-drawn illustrations?"
And I found the answer. Yes, it is possible... but not to counter it but rather to supplement it. This will result in an alloy of logic and intuition, reason and imagination, professionalism and teaching enthusiasm... from which everyone will benefit.
Of course, our main goal is to help (not solve) the OP's problem with some guidance to find a solution. I have convinced myself that the best way to do this is to show how we ourselves can come to a decision in several possible ways. Thus, we will show some universal comprehension techniques that OP may apply in the future to other unfamiliar circuits.
1. What is a diode? First, we need to come up with a functional idea of the diode as an element.
Voltage source. The main feature of a diode is that at a certain voltage applied to it, it begins to keep it (relatively) constant. So diodes can act as voltage stabilizers. Thus they resemble voltage sources and this led to the idea that diodes can be modeled (emulated) by equivalent voltage sources.
The problem is that they are not sources since they do not "produce" energy but rather consume it... they are passive elements like resistors. Unlike sources, their IV curves necessarily pass through the origin of the coordinate system, which means that when there is no voltage there is no current. So, if we blindly replace them by voltage sources, strange problems can appear in circuits which is very well illustrated in the @Tony Stewart's simulation.
The difference between diodes and voltage sources when keeping constant voltage is that diode can do it only by diverting (more or less) else's current through itself while the voltage source can produce and pass current through the load. In other words, diodes are only sinks while voltage sources are both sinks and sources. For example, imagine a Zener diode stabilizer where the diode is replaced by a voltage source.
Voltage source + switch. So, to fully imitate a (Zener) diode, you can connect a switch in series with the voltage source. An ordinary diode can act as such a switch. An example of such a 5.7 V "Zener diode" can be a protecting 0.7 V diode connected between some logic gate input (anode) and the +5 V power supply (cathode). When the input voltage exceeds 5.7 V, this "composed Zener diode" turns on and fixes the input voltage at 5.7 V (i.e., it acts as a diode clipper or limiter).
Dynamic resistor. The most accurate functional equivalent of a diode is a self-varying (dynamic) resistor that changes its resistance in the opposite direction to the current variations. Thus, according to Ohm's law, the voltage depends both on the current and resistance... and stays constant. The diode behaves as a threshold element (mentioned by @Tony Stewart) that behaves as a short connection (a piece of wire) when the threshold is reached.
2. Structure. After we have developed a functional idea of the diode as an element, let's see what diodes D1 and D2 do in the OP's circuit. At first glance, it resembles two cascaded dynamic voltage dividers. The first is composed by R2 as an upper part and the network R1-D1 as a lower part. The second divider consists of D2 (upper part) and R3 (lower part). The overal gain and accordingly, the OP's transfer graph needed, depends on the state of D1 and D2.
3. Operation. AC supplied diode circuits have different behavior during the positive and negative half-wave. That is why I have drawn two different pictures (the second one is a mirrored copy of the first). The pictures of voltage distribution and current paths are captured at times when the input voltage reaches the minimum and maximum values (i.e., these are instantaneous values). Note the lenghth of voltage bars (in red) is not exactly proportional to voltage values.
Positive half-wave. When the input voltage begins increasing above zero, both diodes are off. Both VA and VB follow VIN; VR3 (out) is zero. At 0.7 V D2 turns on and begins shifting down VA with 0.7 V (R3 "pulls down" point A). The transfer curve is linear with a ratio of K = 1/2 (determined by the voltage divider R2-R3). When VA approaches VZ = 3 V, the Zener diode D1 turns on and begins "pulling down" point B and, more lightly, point A. The curve decreases its slope - K = 1/3 (now determined by the voltage divider R2-R1||R3). So the circuit behaves as a "dynamic voltage divider" that changes its transfer ratio at some moment. It resembles diode functional converters (e.g., converting triangle to sine wave).
Negative half-wave. When the input voltage begins decreasing below zero, VB will be shifted down (under ground) with 0.7 V (across the Zener diode D1) and the curve slope will be determined by the R1-R2 voltage divider (K = 1/2)... and will be linear during the whole time. D2 will not conduct, so there is no output voltage at point C.
I think, after all these explanations, OP (and his/her peers) should be able to draw the transfer curve... or the output voltage in time.