Let’s work through the different parts based on the given information from the function graph.

Part 1: Find $f(-28)$ and $f(-12)$

• From the information you provided, it seems that:
  • $f(-28) = -8$
  • $f(-12) = 12$

Part 2: Find $f(24)$ and $f(0)$

• According to the given data:
  • $f(24) = 8$
  • $f(0) = -4$

Part 3: Is $f(8)$ positive or negative?

• From the graph's behavior or context, it appears that $f(8)$ is positive.

Part 4: Is $f(-28)$ positive or negative?

• From the graph, $f(-28) = -8$, so $f(-28)$ is negative.

Part 5: For what value(s) of $x$ is $f(x) = 0$?

• From the graph or your description, the function crosses the x-axis at $x = -24$, $x = -4$, and $x = 16$. Therefore:
  • The values of $x$ where $f(x) = 0$ are $x = -24, -4, 16$.

Part 6: For what values of $x$ is $f(x) > 0$?

• The function is greater than zero (positive) in intervals where it lies above the x-axis. Based on the graph or context, you would express this as:
  • $f(x) > 0$ for the interval $(-24, -4) \cup (16, \infty)$

Let me know if you need further clarification or additional details!

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Follow-up questions:

1. How do we interpret the intervals of positivity for a piecewise function?
2. How do you determine the values where a function crosses the x-axis?
3. What is the difference between $f(x) > 0$ and $f(x) \geq 0$?
4. How can you estimate function values from a graph if the values are not explicitly labeled?
5. What does the behavior of a function near the x-axis tell you about its roots or zeroes?

Tip: Always carefully observe the graph around the x-axis to identify where the function touches or crosses the axis; this will help in finding roots or zeroes.