Domain:

The domain of a function is the set of all possible $x$-values for which the function is defined.

In the provided graph, the function appears to extend infinitely in both the positive and negative directions along the $x$-axis. This means that the function is defined for all real numbers.

• Domain: $(-\infty, \infty)$

Range:

The range of a function is the set of all possible $y$-values that the function can take.

In this graph, the lowest point occurs at $y = 1$ (the vertex of the "V" shape), and the function increases without bound in both directions as $y$ increases.

• Range: $[1, \infty)$

Final Answer:

• Domain: $(-\infty, \infty)$
• Range: $[1, \infty)$

Would you like more details on determining the domain and range, or have any further questions?

Questions to Explore:

1. How would the domain and range change if the graph were shifted downward by 3 units?
2. What would the domain and range be if the vertex of the graph were moved to $(-2, 4)$?
3. How would the range be affected if the graph were reflected over the x-axis?
4. Can you identify the domain and range of the function $f(x) = \sqrt{x - 2} + 1$?
5. What happens to the domain and range if the graph is stretched vertically by a factor of 2?

Tip:

To quickly determine the range of an absolute value function, focus on the vertex (minimum or maximum point) and the direction in which the graph opens. This will help you understand the minimum or maximum value that $y$ can attain.