Let's analyze the graph in the image to determine the domain of the function. The domain refers to the set of all possible values for $x$, for which the function has defined values.

Looking at the graph:

• The function starts at $x = -1$ and ends at $x = 5$.
• For $x$ values within this range, the function is defined.
• The vertical extent of the graph (the range of $y$) does not impact the domain, so we focus on the horizontal axis.

The domain of the function is therefore $x$ values in the interval $[-1, 5]$.

From the given options, the correct domain expression is:

E: $D = \{ x \mid -1 \leq x \leq 5, x \in \mathbb{R} \}$

Would you like further clarification on this?

Here are some related questions to deepen the understanding:

1. What is the difference between domain and range in a function?
2. How can we determine the domain of a function from its graph?
3. What would the range of this function be based on the graph?
4. How do open and closed intervals affect the domain of a function?
5. Can a function have an infinite domain? Give an example.

Tip: Always check if the graph has any breaks or undefined sections to accurately determine the domain.