The graph provided contains two curves: a solid black graph and a dotted orange graph. Based on the structure of the question, we are trying to determine a function that represents the dotted graph based on the given function $y = f(x)$, which is represented by the solid black graph.

Observing the Graph:

1. Solid Black Graph ( $f(x)$ ):

   • The solid black graph seems to start from the origin and increase in the positive direction for both $x$ and $y$. This suggests that $f(x)$ could be a logarithmic or square root function. The behavior resembles a square root function, typically in the form $y = \sqrt{x}$.

2. Dotted Orange Graph:

   • The dotted orange graph appears to be a reflection of the solid black graph over the $x$-axis. This indicates that the dotted graph could be the negative version of the solid graph. If the solid graph is $y = f(x)$, the dotted graph likely represents $y = -f(x)$.

Conclusion:

If $f(x) = \sqrt{x}$, then the dotted graph represents the function: $y = -f(x) = -\sqrt{x}$

Would you like further details or clarification on this explanation?

Here are 5 questions that expand on this topic:

1. What transformations would occur if the graph was reflected over the $y$-axis instead of the $x$-axis?
2. How would the graph change if we applied a vertical stretch to $f(x)$?
3. What happens to the graph if we add or subtract a constant to $f(x)$?
4. How would the graph behave if $f(x)$ was squared (i.e., $f(x)^2$)?
5. Can the dotted graph be shifted horizontally or vertically to coincide with the solid black graph?

Tip: Reflections across the axes change the sign of either $x$ or $y$, depending on which axis the reflection occurs over.