Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Question
![**Problem Statement:**
Find all the \( x \)-values that make the function negative \((f(x) < 0 \text{ when } x = ?)\). Enter your answer in interval notation. Enter \(-\infty\) as -INF, \(\infty\) as INF, and \(\cup\) (union) as U.
Enter the values of \( x \) from smallest to largest.
---
**Question:**
\( f(x) < 0 \) when \( x \) is:
---
**Answer Box:**
\((-∞, -4) \cup (1, 4)\)
---
**Feedback:**
The answer provided is marked as Incorrect. You have 1 try out of 99.
---
**Notes:**
- Use interval notation to indicate ranges of \( x \) where the function \( f(x) \) is negative.
- The interval \((-∞, -4)\) indicates \( x \) values less than \(-4\).
- The interval \((1, 4)\) indicates \( x \) values between \(1\) and \(4\), not including \(1\) or \(4\).
- The use of \(\cup\) indicates a union, meaning solutions can be in either interval.
**Action:**
Make sure your answer accurately reflects the conditions under which \( f(x) \) is negative, and consider revisiting any function information or graphs if available to ensure the solution is correct.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff45c19df-63c8-424a-8751-71766b5c8404%2Ff51f21c4-bc53-48c7-8b89-b6d34c0a83f9%2Fms1qws_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find all the \( x \)-values that make the function negative \((f(x) < 0 \text{ when } x = ?)\). Enter your answer in interval notation. Enter \(-\infty\) as -INF, \(\infty\) as INF, and \(\cup\) (union) as U.
Enter the values of \( x \) from smallest to largest.
---
**Question:**
\( f(x) < 0 \) when \( x \) is:
---
**Answer Box:**
\((-∞, -4) \cup (1, 4)\)
---
**Feedback:**
The answer provided is marked as Incorrect. You have 1 try out of 99.
---
**Notes:**
- Use interval notation to indicate ranges of \( x \) where the function \( f(x) \) is negative.
- The interval \((-∞, -4)\) indicates \( x \) values less than \(-4\).
- The interval \((1, 4)\) indicates \( x \) values between \(1\) and \(4\), not including \(1\) or \(4\).
- The use of \(\cup\) indicates a union, meaning solutions can be in either interval.
**Action:**
Make sure your answer accurately reflects the conditions under which \( f(x) \) is negative, and consider revisiting any function information or graphs if available to ensure the solution is correct.
![Title: Analyzing the Graph of Function \( f \)
Introduction:
The graph above represents the function \( f \). Use the features and behavior of this curve to answer various questions about the function.
Description of the Graph:
- The graph shows a polynomial curve drawn in red.
- The curve extends horizontally from \( x = -9 \) to \( x = 9 \) and vertically from \( y = -9 \) to \( y = 9 \).
- The function exhibits a local maximum at approximately \( x = -5 \), reaching just above \( y = 4 \).
- The graph dips to a local minimum between \( x = 1 \) and \( x = 2 \) going below \( y = -3 \).
- The function increases steeply again beyond \( x = 2 \).
Axes and Grid:
- The horizontal axis (x-axis) ranges from \(-9\) to \(9\).
- The vertical axis (y-axis) ranges from \(-9\) to \(9\).
- Each square on the grid represents 1 unit on both axes.
Key Points for Analysis:
1. **Zeros of the Function:** Identify where the graph intersects the x-axis.
2. **Local Maxima and Minima:** Observe the peaks and troughs of the graph.
3. **End Behavior:** Note the direction of the graph as it approaches the edges of the grid.
4. **Intervals of Increase and Decrease:** Determine where the graph is rising or falling.
Conclusion:
The graph provides valuable insights into the behavior of function \( f \). By studying this graph, one can deduce crucial features such as critical points and regions of change, essential for a deeper understanding of polynomial functions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff45c19df-63c8-424a-8751-71766b5c8404%2Ff51f21c4-bc53-48c7-8b89-b6d34c0a83f9%2Fksef4wk_processed.png&w=3840&q=75)
Transcribed Image Text:Title: Analyzing the Graph of Function \( f \)
Introduction:
The graph above represents the function \( f \). Use the features and behavior of this curve to answer various questions about the function.
Description of the Graph:
- The graph shows a polynomial curve drawn in red.
- The curve extends horizontally from \( x = -9 \) to \( x = 9 \) and vertically from \( y = -9 \) to \( y = 9 \).
- The function exhibits a local maximum at approximately \( x = -5 \), reaching just above \( y = 4 \).
- The graph dips to a local minimum between \( x = 1 \) and \( x = 2 \) going below \( y = -3 \).
- The function increases steeply again beyond \( x = 2 \).
Axes and Grid:
- The horizontal axis (x-axis) ranges from \(-9\) to \(9\).
- The vertical axis (y-axis) ranges from \(-9\) to \(9\).
- Each square on the grid represents 1 unit on both axes.
Key Points for Analysis:
1. **Zeros of the Function:** Identify where the graph intersects the x-axis.
2. **Local Maxima and Minima:** Observe the peaks and troughs of the graph.
3. **End Behavior:** Note the direction of the graph as it approaches the edges of the grid.
4. **Intervals of Increase and Decrease:** Determine where the graph is rising or falling.
Conclusion:
The graph provides valuable insights into the behavior of function \( f \). By studying this graph, one can deduce crucial features such as critical points and regions of change, essential for a deeper understanding of polynomial functions.
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