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,...
Related questions
Topic Video
Question
im confused how to do this practice question. can you help?
![### Exploring Functions: Identifying Relationships
Below are five distinct relationships between \( x \) and \( y \). Your task is to determine which of these relationships qualify as functions. Recall that for a relation to be a function, each input value \( x \) should correspond to exactly one output value \( y \).
#### 1. Tabular Representation
The first relationship is represented in a table format:
| \( x \) | \( y \) |
|--------|--------|
| 0 | -2 |
| 1 | -2 |
| 2 | -2 |
| 3 | -2 |
Each input \( x \) (0, 1, 2, 3) maps to exactly one output \( y \) (-2).
#### 2. Graphical Representation (Parabola)
The second relationship is shown as a graph of a quadratic equation:
![Graph](image_url)
This graph displays a parabola opening upwards. Since a vertical line can intersect a parabola in more than one location, it does not meet the criteria for a function.
#### 3. Set of Ordered Pairs
The third relationship is depicted as a collection of ordered pairs:
\[ \{(0, 1), (1, 2), (2, 3), (3, 4), (4, 5), (5, 6), (6, 7), (7, 8), (8, 9), (9, 10)\} \]
Each pair with a unique input \( x \) yields a unique output \( y \).
#### 4. Mapping Diagram
The fourth representation uses a mapping diagram:
![Mapping Diagram](image_url)
The mapping diagram displays inputs \( x \) (1, 2) connected to various outputs \( y \) (-3, -2, -1, 0, 1). Since one input can connect to multiple outputs, this is not a function.
#### 5. Algebraic Expression
The fifth relationship is given as an algebraic equation:
\[ y = 3.5x \]
This equation indicates a linear relationship where each \( x \) value corresponds to exactly one \( y \) value.
### Analysis and Identification
From these representations, identify which among them qualify as functions based on the definition of a function. Select all that apply.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb04d7cfc-761f-4d3b-a3de-65742cba7b63%2F4f86db3b-cfff-40a0-a7de-b7a2efe39fcc%2F46exehs_processed.png&w=3840&q=75)
Transcribed Image Text:### Exploring Functions: Identifying Relationships
Below are five distinct relationships between \( x \) and \( y \). Your task is to determine which of these relationships qualify as functions. Recall that for a relation to be a function, each input value \( x \) should correspond to exactly one output value \( y \).
#### 1. Tabular Representation
The first relationship is represented in a table format:
| \( x \) | \( y \) |
|--------|--------|
| 0 | -2 |
| 1 | -2 |
| 2 | -2 |
| 3 | -2 |
Each input \( x \) (0, 1, 2, 3) maps to exactly one output \( y \) (-2).
#### 2. Graphical Representation (Parabola)
The second relationship is shown as a graph of a quadratic equation:
![Graph](image_url)
This graph displays a parabola opening upwards. Since a vertical line can intersect a parabola in more than one location, it does not meet the criteria for a function.
#### 3. Set of Ordered Pairs
The third relationship is depicted as a collection of ordered pairs:
\[ \{(0, 1), (1, 2), (2, 3), (3, 4), (4, 5), (5, 6), (6, 7), (7, 8), (8, 9), (9, 10)\} \]
Each pair with a unique input \( x \) yields a unique output \( y \).
#### 4. Mapping Diagram
The fourth representation uses a mapping diagram:
![Mapping Diagram](image_url)
The mapping diagram displays inputs \( x \) (1, 2) connected to various outputs \( y \) (-3, -2, -1, 0, 1). Since one input can connect to multiple outputs, this is not a function.
#### 5. Algebraic Expression
The fifth relationship is given as an algebraic equation:
\[ y = 3.5x \]
This equation indicates a linear relationship where each \( x \) value corresponds to exactly one \( y \) value.
### Analysis and Identification
From these representations, identify which among them qualify as functions based on the definition of a function. Select all that apply.
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.Recommended textbooks for you
![Algebra and Trigonometry (6th Edition)](https://www.bartleby.com/isbn_cover_images/9780134463216/9780134463216_smallCoverImage.gif)
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
![Contemporary Abstract Algebra](https://www.bartleby.com/isbn_cover_images/9781305657960/9781305657960_smallCoverImage.gif)
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
![Linear Algebra: A Modern Introduction](https://www.bartleby.com/isbn_cover_images/9781285463247/9781285463247_smallCoverImage.gif)
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
![Algebra and Trigonometry (6th Edition)](https://www.bartleby.com/isbn_cover_images/9780134463216/9780134463216_smallCoverImage.gif)
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
![Contemporary Abstract Algebra](https://www.bartleby.com/isbn_cover_images/9781305657960/9781305657960_smallCoverImage.gif)
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
![Linear Algebra: A Modern Introduction](https://www.bartleby.com/isbn_cover_images/9781285463247/9781285463247_smallCoverImage.gif)
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
![Algebra And Trigonometry (11th Edition)](https://www.bartleby.com/isbn_cover_images/9780135163078/9780135163078_smallCoverImage.gif)
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
![Introduction to Linear Algebra, Fifth Edition](https://www.bartleby.com/isbn_cover_images/9780980232776/9780980232776_smallCoverImage.gif)
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
![College Algebra (Collegiate Math)](https://www.bartleby.com/isbn_cover_images/9780077836344/9780077836344_smallCoverImage.gif)
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education