Here are the graphs of $y = |x|$ (blue) and $y = |x| + 1$ (green) for $x$ ranging from -3 to 3. The graph of $y = |x|$ forms a V-shape centered at the origin, while the graph of $y = |x| + 1$ is the same V-shape but shifted 1 unit upward.

Do you have any questions or would you like further details?

Here are some related questions you might consider:

1. What happens if we shift $y = |x|$ down instead of up?
2. How would the graph change if we added a horizontal shift, such as $y = |x - 2|$?
3. Can you express the function $y = |x| + c$ in terms of piecewise functions?
4. What if we multiply $y = |x|$ by a constant, such as $y = 2|x|$?
5. How can we use transformations to graph more complex functions of absolute values?

Tip: Shifting the graph of a function vertically by $c$ units simply adds or subtracts $c$ from the function's output.