To determine the domain and range from the graph in the image, let's break down the steps:

Domain

The domain refers to the set of all possible input values (x-values) that the function can take.

1. Observing the x-values from the graph:
   • The function starts around $x = -10$ and continues up to $x = 10$.
   • There are no breaks or holes in the graph, so the domain includes all values between $-10$ and $10$.

Therefore, the domain in interval notation is: $\text{Domain} = [-10, 10]$

Range

The range refers to the set of all possible output values (y-values) the function can produce.

2. Observing the y-values from the graph:
   • The minimum y-value appears to be $-9$ (at the bottom of the graph).
   • The maximum y-value reaches $5$.

Therefore, the range in interval notation is: $\text{Range} = [-9, 5]$

Final Answer

• Domain: $[-10, 10]$
• Range: $[-9, 5]$

Let me know if you would like more detailed explanations or have further questions!

Related Questions:

1. What is the difference between domain and range?
2. How can we determine the domain and range for a piecewise function?
3. How do vertical asymptotes affect the domain of a function?
4. How can graph discontinuities (like holes or breaks) affect the domain and range?
5. What are common mistakes students make when identifying the range from a graph?

Tip:

Always check for any breaks, gaps, or restrictions in a graph, as these can limit the domain or range.