Let's clarify the two equations you provided.

1. $y = |x|$: This equation represents the absolute value of $x$. The graph is a V-shaped curve that opens upwards, with its vertex at the origin $(0, 0)$.

2. $y = |x| + \text{(missing part)}$: It seems like the second equation is incomplete. To proceed, I'll assume you meant something like $y = |x| + k$, where $k$ is a constant. Let me know if this assumption is correct or provide the missing value for a more accurate graph.

For now, I will plot the graph of $y = |x|$ and $y = |x| + 1$ for the values of $x$ from $-3$ to $3$.

Let me generate the graph for you.Here is the graph of the equations $y = |x|$ and $y = |x| + 1$ for the values of $x$ from $-3$ to $3$:

• The blue curve represents $y = |x|$.
• The red curve represents $y = |x| + 1$, which is simply a vertical shift of the blue curve by 1 unit upwards.

Would you like more details on how these graphs were constructed or have any other questions?

Here are five related questions to expand your understanding:

1. What happens to the graph of $y = |x|$ if we add different constants (e.g., $y = |x| + 2$)?
2. How does the graph of $y = |x| - 1$ compare to the original $y = |x|$?
3. What is the effect of multiplying $x$ by a constant in the absolute value function (e.g., $y = |2x|$)?
4. How does the graph of $y = -|x|$ differ from $y = |x|$?
5. What transformations occur if we add a constant to the $x$ value, such as $y = |x + 2|$?

Tip: In absolute value functions, adding a constant to the outside shifts the graph vertically, while adding to the inside shifts it horizontally.