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
28)
![For the graph of the function \( f \) sketched in the figure, determine the following:
**Graph Description:**
The graph is labeled with several important points. The curve passes through the points \((-3, -2)\), \((-1, 1)\), \((\frac{1}{2}, 1)\), \((1, 0)\), \((2, 1)\), and ends at \((4, 2)\). The curve appears to be a continuous function spanning from \(x = -3\) to \(x = 4\).
- The function decreases to a minimum at \((-3, -2)\), then increases to \((-1, 1)\).
- It stays constant through \((-\frac{1}{2}, 1)\) and \((2, 1)\).
- The function decreases again at \((1, 0)\) and rises to reach \((4, 2)\).
**Question (a):** Domain:
- The domain options are given as:
- \((-3, 4)\)
- \([-3, 4]\)
- \([-4, 4]\)
- \([-2, 2]\)
- \((-2, 2)\)
The correct choice, as indicated, is \([-3, 4]\), meaning the function is defined for all \(x\) values from \(-3\) to \(4\) inclusive.
**Question (b):** Range:
- The range options are given as:
- \((-2, 2)\)
- \([-4, 4]\)
- \([-2, 2]\)
The correct choice, as indicated, is \([-2, 2]\), meaning the function's output or \(y\)-values range from \(-2\) to \(2\) inclusive.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd993aba2-7233-4522-8589-0658d060e091%2Fe40349b8-e110-4a10-8e0b-5d1c2bd32151%2Fmb8afna_processed.jpeg&w=3840&q=75)
Transcribed Image Text:For the graph of the function \( f \) sketched in the figure, determine the following:
**Graph Description:**
The graph is labeled with several important points. The curve passes through the points \((-3, -2)\), \((-1, 1)\), \((\frac{1}{2}, 1)\), \((1, 0)\), \((2, 1)\), and ends at \((4, 2)\). The curve appears to be a continuous function spanning from \(x = -3\) to \(x = 4\).
- The function decreases to a minimum at \((-3, -2)\), then increases to \((-1, 1)\).
- It stays constant through \((-\frac{1}{2}, 1)\) and \((2, 1)\).
- The function decreases again at \((1, 0)\) and rises to reach \((4, 2)\).
**Question (a):** Domain:
- The domain options are given as:
- \((-3, 4)\)
- \([-3, 4]\)
- \([-4, 4]\)
- \([-2, 2]\)
- \((-2, 2)\)
The correct choice, as indicated, is \([-3, 4]\), meaning the function is defined for all \(x\) values from \(-3\) to \(4\) inclusive.
**Question (b):** Range:
- The range options are given as:
- \((-2, 2)\)
- \([-4, 4]\)
- \([-2, 2]\)
The correct choice, as indicated, is \([-2, 2]\), meaning the function's output or \(y\)-values range from \(-2\) to \(2\) inclusive.
![The image displays a section of an online assignment containing multiple-choice and fill-in-the-blank questions related to a mathematical function \( f(x) \).
**(b) Range:**
A multiple-choice question asking for the range of the function. The options are:
1. \( (-2, 2) \)
2. \( [-4, 4] \)
3. \( [-2, 2] \) (This is selected with a checkmark)
4. \( [-3, 4] \)
5. \( (-3, 4) \)
**(c) \( f(1) \)**
A fill-in-the-blank question that asks for the value of \( f(1) \). The response given is "0", which is marked as correct with a checkmark.
**(d) All \( x \) such that \( f(x) = 1 \)**
A fill-in-the-blank question asking for all values of \( x \) such that \( f(x) = 1 \). The response given is "0", which is marked with a cross, indicating it is incorrect.
**(e) All \( x \) such that \( f(x) > 1 \)**
A multiple-choice question asking for all values of \( x \) such that \( f(x) > 1 \). The options are:
1. \( (-3, -1) \cup \left( \frac{1}{2}, 1 \right) \)
2. \( (-1, \frac{1}{2}) \)
3. \( (-3, 1) \cup (1, 4) \)
4. \( \left(-1, \frac{1}{2}\right) \cup (2, 4) \) (This is selected)
5. \( (-2, 0) \cup (1, 2) \)
This section of the assignment tests students' understanding of function range, evaluation, and solving inequalities related to functions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd993aba2-7233-4522-8589-0658d060e091%2Fe40349b8-e110-4a10-8e0b-5d1c2bd32151%2Fcva73j_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The image displays a section of an online assignment containing multiple-choice and fill-in-the-blank questions related to a mathematical function \( f(x) \).
**(b) Range:**
A multiple-choice question asking for the range of the function. The options are:
1. \( (-2, 2) \)
2. \( [-4, 4] \)
3. \( [-2, 2] \) (This is selected with a checkmark)
4. \( [-3, 4] \)
5. \( (-3, 4) \)
**(c) \( f(1) \)**
A fill-in-the-blank question that asks for the value of \( f(1) \). The response given is "0", which is marked as correct with a checkmark.
**(d) All \( x \) such that \( f(x) = 1 \)**
A fill-in-the-blank question asking for all values of \( x \) such that \( f(x) = 1 \). The response given is "0", which is marked with a cross, indicating it is incorrect.
**(e) All \( x \) such that \( f(x) > 1 \)**
A multiple-choice question asking for all values of \( x \) such that \( f(x) > 1 \). The options are:
1. \( (-3, -1) \cup \left( \frac{1}{2}, 1 \right) \)
2. \( (-1, \frac{1}{2}) \)
3. \( (-3, 1) \cup (1, 4) \)
4. \( \left(-1, \frac{1}{2}\right) \cup (2, 4) \) (This is selected)
5. \( (-2, 0) \cup (1, 2) \)
This section of the assignment tests students' understanding of function range, evaluation, and solving inequalities related to functions.
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