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

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.

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

Explore the graphs of y=|x| and y=|x|+1 over the interval x from -3 to 3. This problem demonstrates the concept of absolute value functions and how vertical shifts affect their graphs. Perfect for students in Grades 7-10, with step-by-step explanations.

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