https://file.aiquickdraw.com/mathbot/file/1726504958540m4y0hwju.jpg

The image shows a graph of an absolute value function, which has a V-shape. The vertex of the graph is at the origin (0, 0), and the function opens upwards.

For absolute value functions of the form \( f(x) = |x| \), the range consists of all possible \( y \)-values that the function can take. Since absolute value functions are always non-negative, the graph starts at \( y = 0 \) and goes upwards.

**Range**: The range of this absolute value function is:
\[
[0, \infty)
\]
This means the function can take any value from 0 and higher.

Would you like further explanation or have any questions?

Here are five related questions for further exploration:
1. How do you find the domain of an absolute value function?
2. What are the properties of the vertex of an absolute value function?
3. How does shifting an absolute value function vertically affect its range?
4. What is the difference between the range of \( |x| \) and \( -|x| \)?
5. How can we solve equations involving absolute value functions?

**Tip:** The range of any absolute value function \( f(x) = |x| + k \) is always \( [k, \infty) \) when the graph opens upwards.

What is the range of the absolute value function?

Discover the range of an absolute value function with a V-shaped graph. This problem explains the concept of range for absolute value functions, highlighting how the range begins at y = 0 and extends upwards. Suitable for Grades 7-9 math students.

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