Here are the graphs of the two functions:

1. $f(x) = |x| + 3x$: This function shows a V-shape with the left side sloping down and the right side sloping up more steeply due to the $3x$ term.
2. $f(x) = 2|x| - 4$: This function also creates a V-shape but is shifted down by 4 units, with both branches of the graph rising, though less steeply than the first graph.

Would you like more details or have any questions?

Here are some follow-up questions related to this topic:

1. How do absolute value functions generally affect the graph of a function?
2. What is the significance of the term $3x$ in the first function?
3. How does the transformation $-4$ affect the graph in the second function?
4. What would happen if the constant terms were removed from both functions?
5. Can you analyze how symmetry plays a role in both graphs?

Tip: Always check for points of intersection with the x-axis (roots) to better understand graph behavior.