It looks like the function $g(x)$ you provided might contain a typographical error. If the function is intended to be $g(x) = 3x + 8$, here's an analysis:

Properties of $g(x) = 3x + 8$:

1. Linear Function: $g(x)$ is a linear equation.
2. Slope: The coefficient of $x$, which is 3, represents the slope. This means the line rises by 3 units for every 1 unit increase in $x$.
3. Y-Intercept: The constant $8$ is the y-intercept, where the graph crosses the $y$-axis ($g(0) = 8$).
4. Domain and Range: The domain and range of $g(x)$ are both all real numbers ($\mathbb{R}$).
5. Increasing Function: Since the slope is positive ($3 > 0$), $g(x)$ is strictly increasing.

If this was not your intended function, please provide clarification or a corrected version.

Would you like further details about graphing or solving related problems? Here are five follow-up questions for deeper exploration:

1. What is the value of $g(x)$ when $x = 2$?
2. How do you determine the x-intercept of the function $g(x) = 3x + 8$?
3. What transformations occur if the function is modified to $g(x) = 3x - 5$?
4. Can you derive the inverse of the function $g(x) = 3x + 8$?
5. How would the graph of $g(x)$ change if the slope was negative?

Tip: When working with linear functions, always identify the slope and intercept as key features—they provide the structure of the graph and behavior of the function.