https://file.aiquickdraw.com/mathbot/file/17259280831958o4hklfz.jpg

To find the range of the function graphed, we need to analyze the values of \( y \) for which the graph has corresponding \( x \) values.

From the graph, we can observe that it represents a piecewise linear function, often associated with the absolute value function. The graph has two lines: 
1. One line with a negative slope extending from \((-\infty, \infty)\) through the point \((0, 5)\).
2. Another line with a positive slope extending from \((0, 5)\) through \((\infty, \infty)\).

The vertex of the V-shaped graph is at the point \((0, 5)\).

### Range Analysis
The lowest point on the graph is \( y = 5 \) at \( x = 0 \). As \( x \) moves away from zero in either direction (positive or negative), the value of \( y \) increases indefinitely. Therefore, the function does not have any lower bound for \( y \) less than 5 but extends to positive infinity as \( x \) increases or decreases.

Thus, the range of the function is:
\[ \boxed{[5, \infty)} \]

Would you like any more details or have any questions about this problem? Here are some related questions you might find interesting:

1. What is the domain of the function depicted in the graph?
2. How would you express the function algebraically based on the graph?
3. What is the slope of each segment of the piecewise function?
4. How does shifting the vertex of the graph affect the range?
5. Can the range of the function change if it is translated vertically?

**Tip:** To find the range of a function graphically, look for the lowest and highest \( y \)-values that the function can attain.

Discover how to find the range of a piecewise function from a V-shaped graph. The graph depicts an absolute value function with vertex at (0, 5), extending towards infinity. Learn how the range is calculated as [5, ∞). Suitable for students in Grades 8-10.

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