Draw the graph of y=|x| and y=|x|+ for the values of x from - 3 to 3

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.

Draw the graph of y=|x| and y=|x|+ for the values of x from -3 to 3

Explore how to graph the absolute value functions y=|x| and y=|x|+k over the range of x values from -3 to 3. This problem focuses on key algebraic concepts such as absolute value functions and their vertical shifts, suitable for students in Grades 6-8.

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