The problem asks to compare two functions based on line symmetry.

• f(x) (on the left) represents a straight line. A straight line, unless it's vertical or horizontal, does not have line symmetry. Therefore, the correct answer for $f(x)$ is "none."

• g(x) (on the right) represents a parabola, which opens upwards. Parabolas are symmetrical around their vertex, and the line of symmetry is vertical, passing through the vertex. Here, the vertex appears to be at $x = 0$. Therefore, the line of symmetry for $g(x)$ is $x = 0$.

Final answers:

• $f(x)$: none
• $g(x)$: $x = 0$

Would you like further details or have any questions?

Here are 5 related questions for further exploration:

1. What is the general equation for a line, and how can we identify symmetry?
2. What is the general form of a quadratic function, and how do you find its vertex and symmetry line?
3. Are there cases where a linear function can have symmetry? If so, when?
4. How does the graph of a function help in understanding its symmetry?
5. Can functions have more than one line of symmetry?

Tip: For any parabola, the line of symmetry is always a vertical line passing through the vertex of the parabola.