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 which option best represents the functions $f(x)$ and $g(x)$, we analyze the provided graph of $y = f(x) + g(x)$. The graph indicates two key features:

1. Behavior at Intersection: The graph crosses the x-axis, implying that $f(x)$ and $g(x)$ have opposite signs. At the intersection points, one function is positive and the other is negative. This characteristic must be reflected in the options provided.

2. Overall Shape: The general shape of the curve suggests that one function could be a parabola and the other could be a linear function. The overall upward curve after the minimum point indicates that $f(x)$ could be a convex function and $g(x)$ could be a linear function intersecting it.

Analyzing options A, B, C, and D:

• Option A: This has the appropriate convex nature but does not reflect the intersection behavior correctly.
• Option B: This shows one function with a different shape and also fails the intersection behavior.
• Option C: This represents intersecting behaviors incorrectly.
• Option D: This shows the correct concave up structure that matches with the behavior of $f(x)$ and $g(x)$.

Thus, the best representation is A.