https://file.aiquickdraw.com/mathbot/file/17260276629311bp98e7s.jpg

Let's analyze the image of the graph and questions to provide assistance:

The question you're working on is about using the graph of the function \( f(x) \) to answer several parts. Specifically, the visible parts include:

1. (c) Is \( f(4) \) positive or negative?
2. (d) Is \( f(-6) \) positive or negative?
3. (e) For what value(s) of \( x \) is \( f(x) = 0 \)?

### Part (c): \( f(4) \)
Look at \( x = 4 \) on the graph. The corresponding \( y \)-value at \( x = 4 \) will determine if \( f(4) \) is positive or negative. From the image, \( f(4) \) appears to be around 2, which is positive.

- **Answer: Positive**

### Part (d): \( f(-6) \)
Now, check \( x = -6 \) on the graph. The point on the graph corresponding to \( x = -6 \) seems to be just below the x-axis, which means \( f(-6) \) is negative.

- **Answer: Negative**

### Part (e): For what value(s) of \( x \) is \( f(x) = 0 \)?
You need to find the \( x \)-values where the graph crosses the x-axis. From the graph, it appears that \( f(x) = 0 \) at the following points:
- \( x = -12 \)
- \( x = -4 \)
- \( x = 2 \)
- \( x = 8 \)

- **Answer: \( x = -12, -4, 2, 8 \)**

Let me know if you'd like further details or have any questions!

Here are 5 related questions for practice:
1. What is the value of \( f(2) \)?
2. For what value(s) of \( x \) is \( f(x) > 0 \)?
3. For what value(s) of \( x \) is \( f(x) < 0 \)?
4. What are the local maxima and minima of the function based on the graph?
5. What is the approximate slope of the graph between \( x = -6 \) and \( x = 0 \)?

**Tip:** When analyzing graphs, always pay close attention to where the graph crosses the axes to determine key points such as zeros (where \( f(x) = 0 \)) and intercepts.

Is f(4) positive or negative? Is f(-6) positive or negative? For what value(s) of x is f(x) = 0?

Learn how to analyze a function's graph to determine positivity, negativity, and zeros. This problem covers important concepts in graphing functions and interpreting function behavior based on graph intersections.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation