Here is the graph of the piecewise function $g(x)$. The graph consists of three parts:

1. The blue line represents $g(x) = -8|x|$ for $x \leq -1$, which decreases steeply as $x$ moves further left.
2. The green line represents $g(x) = 9x + 5$ for $-1 < x < 3$, showing a steep upward slope.
3. The red horizontal line represents $g(x) = -3$ for $x \geq 3$, which is constant.

Would you like a further explanation or have any specific questions about this graph?

Here are 5 related questions you can explore:

1. How would the graph change if the coefficient of $|x|$ were different in the first piece?
2. What happens if you change the slope of the middle function from $9x + 5$ to another linear function?
3. How can you determine the continuity of this piecewise function?
4. How would the domain restrictions on each piece affect the graph if they were altered?
5. What are the points of intersection between different parts of the function?

Tip: When analyzing piecewise functions, always check for continuity at the boundary points to determine if the graph has jumps or gaps.