Let's break down the analysis of the graph provided for $y = f(x)$.

1. Domain:

The domain is the set of all $x$-values for which the function is defined. By observing the graph:

• The function starts at $x = -4$ (closed circle, included point), and ends at $x = 5$ (open circle, excluded point). Thus, the domain is: $\text{Domain: } [-4, 5)$

2. Range:

The range is the set of all possible $y$-values of the function. From the graph:

• The minimum $y$-value is $0$, occurring at $x \approx 4.5$, and the maximum $y$-value is $8$, occurring at $x = -2$. Thus, the range is: $\text{Range: } [0, 8]$

3. Intervals of Increase, Decrease, and Constant:

• Increasing: The function is increasing where the slope of the curve is positive.

  • From $x = -4$ to $x = -2$, the function is increasing.
  • From $x \approx 3$ to $x = 5$, the function is also increasing.
  • Increasing intervals: $(-4, -2) \cup (3, 5)$

• Decreasing: The function is decreasing where the slope of the curve is negative.

  • From $x = -2$ to $x = 3$, the function is decreasing.
  • Decreasing interval: $(-2, 3)$

• Constant: There is no section where the function is constant.

4. Zeros of $f(x)$ (where $f(x) = 0$):

The zero of the function is where the curve intersects the x-axis (i.e., where $y = 0$).

• From the graph, the zero is located at $x = -3$. Thus, the zero is: $\text{Zero: } x = -3$

Would you like to dive deeper into any specific part of this problem?

Here are some related questions:

1. How would we find the critical points of this function?
2. Can we approximate the derivative of $f(x)$ based on the graph?
3. How do we describe the concavity of the graph?
4. How can we use limits to describe the behavior of the function near $x = 5$?
5. How could the function be modeled algebraically based on the graph?

Tip: When analyzing functions graphically, always check for open and closed endpoints to determine whether certain values are included in the domain or range.