https://file.aiquickdraw.com/mathbot/file/1730670964840oubfjjfh.jpg

Let’s analyze the function \( f(x) \) from the graph to answer each question.

### (a) Is \( f(2) \) negative?
Looking at \( x = 2 \) on the graph, the corresponding \( y \)-value is positive. Thus, \( f(2) \) is **not negative**.

**Answer**: No

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### (b) For which value(s) of \( x \) is \( f(x) = 0 \)?
The function \( f(x) \) equals zero at points where the graph intersects the \( x \)-axis. From the graph, these intersections occur at:
- \( x = -4 \)
- \( x = -1 \)
- \( x = 3 \)

**Answer**: \( x = -4, -1, 3 \)

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### (c) For which value(s) of \( x \) is \( f(x) < 0 \)?
The function \( f(x) \) is negative when the graph is below the \( x \)-axis. From the graph, \( f(x) < 0 \) over the following intervals:
- \( x \in (-\infty, -4) \)
- \( x \in (-1, 3) \)

**Answer**: \( (-\infty, -4) \cup (-1, 3) \)

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Would you like further clarification on any of these answers?

### Related Questions
1. How can we determine if a function is increasing or decreasing from its graph?
2. What does it mean for a function to be concave up or concave down?
3. How do we find the maximum or minimum values of a function from its graph?
4. What are the implications of a function having zero values at specific points?
5. How do we interpret the domain and range of a function from its graph?

### Tip
Always check where the graph crosses the \( x \)-axis for zero values and the intervals above or below the axis for positive and negative values.

Use the graph of the function y = f(x) below to answer the questions:
(a) Is f(2) negative?
(b) For which value(s) of x is f(x) = 0?
(c) For which value(s) of x is f(x) < 0?

Analyze the graph of the function y = f(x) to determine if f(2) is negative, identify the x-values for which f(x) equals zero, and find the intervals where f(x) is less than zero. Suitable for high school students studying function analysis and graph interpretation.

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