Based on the graph you've provided, let's analyze its domain and range.

1. Domain:

The domain of a function represents all possible $x$-values (input values) that the function can take.

• Looking at the graph, the function extends indefinitely to the left and right along the $x$-axis.
• Therefore, the domain appears to cover all real numbers.

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

2. Range:

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

• The graph shows that the function decreases to a value slightly below $-10$ and increases to values beyond $10$.
• There are no upper or lower limits to how high or low the graph can go based on the trend.

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

Would you like any further clarification or more detailed explanation?

Follow-up questions:

1. What is the significance of identifying the domain and range of a function?
2. How do we determine if a function is continuous based on its graph?
3. Could you describe how to find local maxima or minima using this graph?
4. How would you classify the behavior of this function at $x = 0$?
5. What does the increasing or decreasing behavior of the function tell us?

Tip:

When identifying the domain of a function, always check for any vertical asymptotes or breaks in the graph. These indicate where the function is undefined.