The graph depicted in the image is a piecewise linear function $f(x)$. This graph has two distinct linear segments, one with a negative slope and the other with a positive slope. Let's analyze the graph step by step to determine its range:

1. Left Segment: The left segment of the graph starts from the left side and moves towards the origin. As $x$ increases from a negative value, $y$ decreases, moving from a high positive value to a lower value as it approaches the vertex at the origin.

2. Right Segment: The right segment starts from the origin and continues with a positive slope, meaning $y$ increases as $x$ increases.

The vertex (or the point where the two lines meet) occurs at the origin (0,0). From this observation:

• The left segment implies that as $x$ approaches negative infinity, $y$ approaches positive infinity.
• The right segment shows that as $x$ increases, $y$ also increases without bound.

Conclusion on the Range:

• The smallest value of $y$ is at the origin, where $y = 0$.
• There is no upper bound on $y$; as $x$ moves away from the origin in either direction, $y$ increases indefinitely.

Thus, the range of the function $f(x)$ is $\boxed{[0, \infty)}$.

Would you like further details or have any questions? Here are some related questions:

1. How do you find the range of a function given its graph?
2. What is the difference between the domain and the range of a function?
3. How can the vertex of a piecewise function be determined from its equation?
4. How does the slope of a line segment affect the range of a function?
5. What are the implications of a function having an infinite range?

Tip: When analyzing the range of a function graphically, always look for the lowest and highest points on the graph along the $y$-axis to determine the minimum and maximum values $y$ can take.