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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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:

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:

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:

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.
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