Let's analyze the graph and complete the table based on the information provided. The graph shows a function with the following key features:

1. Domain:

The domain of a function is the set of all possible input values (x-values). The graph shows a function that exists for all real x-values. So, the domain is:

• Domain: $(-\infty, \infty)$

2. Range:

The range refers to all the possible output values (y-values). The lowest point on the graph appears to be at $y = -2$, and the function increases without bound. So, the range is:

• Range: $[-2, \infty)$

3. Extrema:

• The function has a local minimum at $x = 0$ and $y = -2$.
• Extrema: Minimum at $(0, -2)$

4. End Behavior:

• As $x \to -\infty$, the function increases without bound (goes to $+\infty$).
• As $x \to \infty$, the function also increases without bound (goes to $+\infty$).
• End Behavior:
  • $\lim_{x \to -\infty} f(x) = \infty$
  • $\lim_{x \to \infty} f(x) = \infty$

5. Increasing and Decreasing Intervals:

• The function is decreasing on $(-\infty, 0)$.
• The function is increasing on $(0, \infty)$.
• Increasing and Decreasing Intervals:
  • Decreasing on $(-\infty, 0)$
  • Increasing on $(0, \infty)$

6. Constant Interval(s):

The function does not have any horizontal segments (constant behavior). Hence:

• Constant Interval(s): None

7. Discontinuities:

The function is continuous throughout, with no breaks or holes. So:

• Discontinuities: None

8. Intercepts:

• The function intercepts the y-axis at $y = -2$ (since at $x = 0$, $f(x) = -2$).
• The function also intercepts the x-axis at $x = 0$ (since the function crosses the x-axis at $y = 0$ at this point).
• Intercepts:
  • y-intercept: $(0, -2)$
  • x-intercept: $(0, 0)$

Let me know if you'd like further explanations or have any additional questions! Here are some related questions for you to consider:

1. How do you determine the range of a function from its graph?
2. What is the significance of extrema in a function's graph?
3. How can you describe end behavior for functions like polynomials?
4. How do increasing and decreasing intervals relate to the slope of the function?
5. What does a discontinuity look like on a graph, and how do you identify it?

Tip: When analyzing a function's graph, it can be helpful to note key features like the vertex, intercepts, and intervals where the function is increasing or decreasing.