Let's analyze the questions based on the graph provided:

Part (a): Is $f(-3)$ positive?

To determine if $f(-3)$ is positive, locate the point where $x = -3$ on the graph and observe the corresponding $y$-value. If the point lies above the $x$-axis, then $f(-3)$ is positive. If it lies on or below the $x$-axis, it is not positive.

Part (b): For which values of $x$ is $f(x) > 0$?

This question asks for the intervals where the graph of $y = f(x)$ is above the $x$-axis. You need to identify these intervals and express them using interval notation.

Part (c): For which values of $x$ is $f(x) = 0$?

This question asks for the $x$-values where the graph intersects the $x$-axis, meaning where $y = 0$. List all such $x$-values.

Analysis:

• Part (a): At $x = -3$, the graph seems to be above the $x$-axis, which means $f(-3)$ is positive. Answer: Yes.

• Part (b): $f(x) > 0$ in the intervals where the graph is above the $x$-axis. This appears to be in the intervals $(-5, -2)$ and $(1, 4)$. Answer: $(-5, -2) \cup (1, 4)$.

• Part (c): The graph intersects the $x$-axis at $x = -5$, $x = -2$, $x = 1$, and $x = 4$. Answer: $x = -5, -2, 1, 4$.

Would you like more details or explanations on any of these parts?

Here are five related questions:

1. How do you determine where a function is increasing or decreasing from its graph?
2. What is the significance of the points where the graph intersects the x-axis?
3. Can a function be positive and decreasing at the same time? Give an example.
4. How would you express the intervals where a function is negative using interval notation?
5. What does it mean for a function to have a zero at a particular value of $x$?

Tip: When working with graphs, always pay close attention to where the graph intersects the axes; this information often provides key insights into the behavior of the function.