The graph provided appears to represent a piecewise linear function, likely an absolute value function or similar. To determine the domain and range of the function from the graph:

Domain:

The domain of a function consists of all the possible input values (typically $x$ values) for which the function is defined.

• Observing the graph, the function extends horizontally from the far left to the far right, with no breaks or undefined points.
• Therefore, the domain of the function is all real numbers:
  $\text{Domain: } (-\infty, \infty)$

Range:

The range of a function consists of all possible output values (typically $y$ values) that the function can take.

• From the graph, the lowest point (minimum $y$) is at $y = 0$, and the function extends upwards.
• The function reaches positive values but does not extend infinitely downward.
• Therefore, the range of the function is all real numbers $y$ such that $y \geq 0$:
  $\text{Range: } [0, \infty)$

Would you like further details or have any questions?

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Relative Questions:

1. What is a piecewise function, and how does it relate to the graph?
2. How do you determine the domain and range for more complex functions?
3. Can you explain how to identify asymptotes from a graph?
4. How would the domain and range change if there was a discontinuity?
5. What role does the vertex of an absolute value function play in determining the range?

Tip: When analyzing the graph of a function, always start by identifying any breaks, jumps, or undefined points in the graph to determine the domain, and look at the minimum and maximum $y$ values to find the range.