Final answer:
To sketch the graph, plot the points P, Q, and R on a coordinate plane and connect them with a smooth curve. This could be a parabola opening downwards or a similar function, but multiple functions might fit these points without more constraints.
Step-by-step explanation:
To sketch the graph of a function with the given properties (P(0, 0), Q(2, 3), R(4, 0)), first plot the points on a coordinate plane. Start with P at the origin (0,0). Move rightward along the x-axis to plot Q at (2,3), which is 2 units right and 3 units up from P. From Q, move further rightward to plot R at (4,0), which is 2 more units to the right from Q and 3 units down, back to the x-axis level.
Next, connect these points with a smooth curve that reflects the nature of the function. The function might resemble a parabola opening downwards or any other function that includes these three points and fits the context of your question (without additional constraints, multiple functions could pass through these points).
By shading the area between 3 < x < 6 or x < 7, we can represent probabilities or cumulative distributions if we are dealing with a probability density function. However, since specific equations are not provided for this context, that step is not demonstrated here.