The correct answer is:

1. Both f(x) and g(x) are functions.

Explanation:

• For a relation to be a function, each input (x) must correspond to exactly one output (y).
• For both f(x) and g(x), the rule is that for each value of $x$, there is a single corresponding value of $y$, as long as the intervals are properly defined for each piece of the function.
  • For $f(x)$, it's split into $x^2$ for $0 \leq x \leq 3$ and $3x$ for $3 \leq x \leq 10$, which does not cause ambiguity.
  • Similarly, for $g(x)$, $x^2$ is defined for $0 \leq x \leq 2$ and $3x$ for $2 \leq x \leq 10$, also without ambiguity.

Thus, both are functions.

Would you like more details or further clarifications on this?

Here are 5 related questions you might find interesting:

1. How do you determine if a piecewise function is a valid function?
2. What are the differences between a function and a relation?
3. How do you handle a situation where a relation is not a function?
4. Can a function have multiple expressions for different intervals of $x$?
5. What is the domain of a piecewise function?

Tip: When checking if a relation is a function, make sure no $x$-value maps to more than one $y$-value!