From the provided image, you are asking for the domain and range of the graphed function.

Domain

The domain of a function consists of all possible input values (x-values). Observing the graph, the function appears to extend indefinitely in both the positive and negative directions along the x-axis. There are no restrictions such as breaks or vertical asymptotes that limit the x-values.

Domain: $(-\infty, \infty)$

Range

The range consists of all possible output values (y-values). Observing the graph:

• The function decreases towards negative infinity as $x \to -\infty$.
• The function reaches a local maximum at approximately $y = 5$.
• The function has no upper bound as $x \to \infty$ (it increases indefinitely).

Range: $(-\infty, \infty)$

Would you like a deeper explanation, or do you have additional questions?

Follow-Up Questions:

1. What happens to the range of a function if there is a vertical asymptote?
2. How would the domain change if the function contained a square root or logarithm?
3. Can the range of a function be finite? Provide an example.
4. How do vertical and horizontal asymptotes impact the domain and range?
5. What tests can confirm if a graph represents a function?

Tip:

To determine the range of a function, look at the lowest and highest points the graph reaches (or extends to) on the y-axis.