Let's analyze the graph and answer the questions step by step:

a) Domain

The domain represents all possible x-values for the function. From the graph, the x-values span from -5 to 7.7. Therefore, the domain is:

$\boxed{[-5, 7.7]}$

b) Range

The range represents all possible y-values for the function. From the graph, the function dips to around $-5$ and reaches as high as $10$. Therefore, the range is:

$\boxed{[-5, 10]}$

c) f(-4)

To find $f(-4)$, look at the graph's value when $x = -4$. From the graph, at $x = -4$, the function is approximately at $f(-4) = 5$.

So, $f(-4) = \boxed{5}$.

d) f(x) = 2

To find where $f(x) = 2$, locate the points where the curve crosses $y = 2$. Based on the graph, this happens at approximately $x = -1.5$ and $x = 5.5$.

Thus, the solutions to $f(x) = 2$ are:

$\boxed{x = -1.5 \text{ and } x = 5.5}$

Would you like more details or clarifications on any of these solutions?

Here are five related questions to explore further:

1. How do you calculate the domain and range of more complex functions?
2. What is the significance of zero crossings (like $f(3) = 0$) in a function's graph?
3. How would you algebraically solve for $x$ when $f(x) = 2$ if the equation was given?
4. How do different types of functions (quadratic, cubic, etc.) affect their domain and range?
5. What methods can be used to graph functions like this one?

Tip: When finding $f(x)$ for specific values of $x$, it's often helpful to read the graph carefully and, if needed, interpolate between points for more accuracy.