Let's analyze the contents of the image step-by-step. The exercise asks to analyze two functions, $g(x)$ and $f(x)$, with the following details provided:

Analyze $g(x)$:

1. Domain: $(-3, 3)$
2. Range: $(-2.2, 1)$
3. Absolute Maximum: Not applicable (N/A)
4. Absolute Minimum: Not applicable (N/A)
5. Intervals of increase and decrease:
   • The intervals of $x$ where $g(x)$ is increasing and decreasing are left to be filled.

Analyze $f(x)$:

Part 1: Function Evaluation

We are asked to evaluate $f(x)$ at specific points, using the graph to the right.

• $f(0)$
• $f(1)$
• $f(2)$
• $f(3)$
• $f(4)$

By analyzing the graph visually:

• $f(0) = 0$
• $f(1) = 1$
• $f(2) = 0$
• $f(3) = -3$
• $f(4) = -1$

Part 2: Additional Information

We are asked to fill in the following about $f(x)$:

1. Domain: Based on the graph, the function seems to be defined for $x \in (-\infty, \infty)$.
2. Range: From the graph, it appears that the range of the function is approximately $[-3, 2]$.
3. X-intercepts (zeros): The graph crosses the x-axis at $x = 0$, $x = 2$, and $x = 3$.
4. Y-intercept: The y-intercept is at $f(0) = 0$.
5. Absolute Maximum: The highest point on the graph is at $f(1) = 1$, so the absolute maximum is $1$.
6. Absolute Minimum: The lowest point on the graph is at $f(3) = -3$, so the absolute minimum is $-3$.
7. Relative Maximum and Minimum:
   • Relative maximum occurs at $x = 1$ where $f(x) = 1$.
   • Relative minimum occurs at $x = 3$ where $f(x) = -3$.
8. Intervals of Increase: The function increases on the interval $(-\infty, -1.5)$ and $(1, 2.5)$.
9. Intervals of Decrease: The function decreases on $(-1.5, 1)$ and $(2.5, \infty)$.
10. Zeros: As mentioned, the zeros are $x = 0$, $x = 2$, and $x = 3$.
11. For what value of $x$ is $f(x)$ discontinuous?: The function appears continuous throughout its domain, so there is no discontinuity.

Would you like further details or explanations on any specific part? Here are five relative questions to explore:

1. How do we determine intervals where the function is increasing or decreasing from a graph?
2. What is the difference between absolute and relative extrema?
3. How can we tell if a function is continuous or discontinuous?
4. Why does $f(x)$ have no absolute maximum or minimum outside the given intervals?
5. How do x-intercepts relate to the zeros of a function?

Tip: When analyzing functions graphically, always check if the function is defined everywhere and if any breaks or holes indicate discontinuities.