To determine the domain and range for the given graph, let's analyze the curve shown in the image.

Domain:

The domain represents all the possible $x$-values (horizontal axis) for which the function is defined.

• The curve starts at $x = 0$ and continues indefinitely to the right.
• Since the graph extends to the right without bound, the domain begins at $x = 0$ and goes to positive infinity.
• The point at $x = 0$ is included, as indicated by the solid dot.

Thus, the domain in inequality notation is: $0 \leq x < \infty$

Range:

The range represents all the possible $y$-values (vertical axis) that the function can take.

• The highest point on the graph is at $y = 2$, and the graph decreases as it moves to the right, approaching $y = -\infty$ without actually reaching it.
• The point at $y = 2$ is included, as indicated by the solid dot.

Thus, the range in inequality notation is: $-\infty < y \leq 2$

Final Answer:

• Domain: $0 \leq x < \infty$
• Range: $-\infty < y \leq 2$

Would you like further details or have any questions about this?

Here are five related questions you might explore:

1. How does changing the slope of the graph affect the domain and range?
2. What would happen to the domain if the graph were reflected over the y-axis?
3. Can a range include negative infinity but not positive infinity?
4. How do you determine the domain and range of a graph with a vertical asymptote?
5. How does the presence of a horizontal asymptote influence the range of a function?

Tip: When identifying the domain and range from a graph, always pay close attention to the direction the curve extends and whether the endpoints are open or closed (solid or hollow circles).