https://file.aiquickdraw.com/mathbot/file/1726840680911mrmu9rmy.jpg

The graph you've provided represents a V-shaped function, which appears to be an absolute value function. The general form of an absolute value function is:

\[
f(x) = a|x - h| + k
\]

From the graph, it seems that the vertex of the function is at the origin, \((0, 0)\), and the function opens downwards. Therefore, we can deduce that this is likely of the form:

\[
f(x) = -|x|
\]

### Range of the function:

Since the graph opens downwards and has its vertex at the origin, the maximum value of \(f(x)\) is 0. The graph extends downward without bound, meaning the function can take any value less than or equal to 0. Therefore, the range of the function is:

\[
\boxed{(-\infty, 0]}
\]

Would you like more details on how this range was determined, or do you have other questions? Here are 5 related questions for deeper exploration:

1. What is the domain of the absolute value function in this graph?
2. How would the range change if the vertex moved above or below the origin?
3. What happens to the range if the function opens upwards instead of downwards?
4. Can you write the equation of this function based on the graph?
5. How does the slope of the graph affect the equation of the absolute value function?

**Tip**: The range of a function refers to the set of all possible output values (y-values) of that function. Always check the direction in which the graph opens to determine if the range is bounded.

This page explores the range of the absolute value function f(x) = -|x| based on a provided graph. The function has its vertex at the origin and opens downward. Learn how to determine the range and other properties of the function, suitable for students in Grades 9-12.

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