The graph of $f(x) = |x|$ is the standard V-shaped absolute value function, while the graph of $g(x) = |x| + 5$ is the same V-shaped function, but shifted 5 units upward.

Relationship:

The graph of $g(x)$ is a vertical translation of $f(x)$. Specifically, $g(x)$ is obtained by moving the graph of $f(x)$ up by 5 units.

Do you want more details or have any questions?

Here are some related questions for further exploration:

1. How would the graph of $g(x) = |x| - 3$ compare to $f(x)$?
2. What happens if you subtract a constant from $|x|$, e.g., $f(x) = |x| - 2$?
3. How would the graph change if you multiply $|x|$ by a constant, say $2|x|$?
4. What is the effect of adding or subtracting from the $x$-variable inside $|x|$?
5. How does the vertex of $f(x) = |x|$ shift with vertical or horizontal translations?

Tip: Vertical shifts occur when constants are added or subtracted to the entire function.