The diagram shows the graph of the sum of the functions $f(x)$ and $g(x)$ - HSC - SSCE Mathematics Extension 1 - Question 4 - 2022 - Paper 1

To determine the correct representations of the graphs $f(x)$ and $g(x)$ that correspond to the given sum $y = f(x) + g(x)$ shown in the diagram, we need to analyze the behavior of the curve.

Considering that the sum of two functions is depicted as a parabola opening upwards, at least one of the functions must also exhibit a minimum or maximum behavior influencing the overall graph.
Hence, we can conclude that the best representation of the individual graphs should consist of at least one parabola and potentially a linear function that adds to the overall parabolic shape.
Looking at the options, we observe:

• Option A has a parabolic appearance that indicates two increasing functions, which seems plausible.
• Option B shows an intersection that might represent cancellation at some point but does not yield a parabolic sum.
• Option C depicts two convex functions that wouldn't form a valid sum.
• Option D contains elements suggesting the right upward behavior in summation, but they do not resonate with the given diagram.

Conclusively, Option A is the most suitable representation of $f(x)$ and $g(x)$, confirming parabolic behavior with linearity suitable for the addition resulting in the depicted sum of functions.