To determine which of the two functions $f(x)$ or $g(x)$ is linear, we need to check if the change in the values of the function is consistent between consecutive values of $x$. In other words, a function is linear if the differences between consecutive values of $f(x)$ or $g(x)$ are constant.

Let's first check the differences for $f(x)$ and $g(x)$.

For $f(x)$:

$f(0) = 0, \quad f(3) = 3, \quad f(6) = 35, \quad f(10) = 57, \quad f(15) = 84$

The differences between consecutive values of $f(x)$:

• $f(3) - f(0) = 3 - 0 = 3$
• $f(6) - f(3) = 35 - 3 = 32$
• $f(10) - f(6) = 57 - 35 = 22$
• $f(15) - f(10) = 84 - 57 = 27$

Since the differences are not consistent, $f(x)$ is not linear.

For $g(x)$:

$g(0) = -1, \quad g(3) = 20, \quad g(6) = 41, \quad g(10) = 69, \quad g(15) = 104$

The differences between consecutive values of $g(x)$:

• $g(3) - g(0) = 20 - (-1) = 21$
• $g(6) - g(3) = 41 - 20 = 21$
• $g(10) - g(6) = 69 - 41 = 28$
• $g(15) - g(10) = 104 - 69 = 35$

Again, the differences are not constant, so $g(x)$ is also not linear.

Conclusion:

Neither $f(x)$ nor $g(x)$ appears to be a linear function based on their changing differences. However, we could recheck or reconsider the problem constraints or context to understand better. Would you like me to verify this further?