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
Question
Which equation is a function and why?
![### Educational Website Content: Graphs and Diagrams
#### 1) Linear Function Graph
This graph displays a straight line passing through points on a Cartesian coordinate system. The key points through which the line passes can be analyzed to determine the equation of the line. Note the intercepts and slope.
#### 2) Quadratic Function Graph
This graph showcases a parabola opening downwards. The vertex of the parabola is located at (-1, 4), and it crosses the x-axis at points (-2, 0) and (0, 0), known as the roots or solutions of the quadratic function.
#### 3) Piecewise Function Graph
This graph illustrates a piecewise function with segments defined in different intervals. One segment goes vertically through x = -2 to x = 0, the second one is horizontal from (-2, -2) to (2, -2), and the third vertical segment up from (2, -2) to (2, 2).
#### 4) Table of Values for a Function
This table shows the relationship between x and y values:
```
x | y
----
1 | 1
2 | 1
3 | 1
```
Here, for any input \( x \), the output \( y \) is always 1.
#### 5) Function Mapping Diagram
This diagram effectively maps inputs to outputs as follows:
- -2 maps to 3,
- 3 maps to 8,
- 4 maps to 8,
- 6 maps to 12.
#### 6) Another Table of Values for a Different Function
Another table indicates the relationship between x and y values:
```
x | y
----
1 | 3
2 | 4
3 | 6
```
Here, the output \( y \) increases as the input \( x \) increases.
#### 7) Set of Ordered Pairs 1
This is a set of ordered pairs:
\[
\{ (1, 1), (2, 2), (3, 1), (3, 2) \}
\]
Each pair represents a point's coordinates on a Cartesian plane.
#### 8) Set of Ordered Pairs 2
This set includes ordered pairs:
\[
\{ (-6, 5), (-3, 8), (-6, 9) \}
\]
These pairs are points that can](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4895c6df-eb5a-4830-9b1e-b00e9a38873d%2F48b94f17-b98e-47b1-b58f-3a8a25db2188%2Fkynyoio_processed.png&w=3840&q=75)
Transcribed Image Text:### Educational Website Content: Graphs and Diagrams
#### 1) Linear Function Graph
This graph displays a straight line passing through points on a Cartesian coordinate system. The key points through which the line passes can be analyzed to determine the equation of the line. Note the intercepts and slope.
#### 2) Quadratic Function Graph
This graph showcases a parabola opening downwards. The vertex of the parabola is located at (-1, 4), and it crosses the x-axis at points (-2, 0) and (0, 0), known as the roots or solutions of the quadratic function.
#### 3) Piecewise Function Graph
This graph illustrates a piecewise function with segments defined in different intervals. One segment goes vertically through x = -2 to x = 0, the second one is horizontal from (-2, -2) to (2, -2), and the third vertical segment up from (2, -2) to (2, 2).
#### 4) Table of Values for a Function
This table shows the relationship between x and y values:
```
x | y
----
1 | 1
2 | 1
3 | 1
```
Here, for any input \( x \), the output \( y \) is always 1.
#### 5) Function Mapping Diagram
This diagram effectively maps inputs to outputs as follows:
- -2 maps to 3,
- 3 maps to 8,
- 4 maps to 8,
- 6 maps to 12.
#### 6) Another Table of Values for a Different Function
Another table indicates the relationship between x and y values:
```
x | y
----
1 | 3
2 | 4
3 | 6
```
Here, the output \( y \) increases as the input \( x \) increases.
#### 7) Set of Ordered Pairs 1
This is a set of ordered pairs:
\[
\{ (1, 1), (2, 2), (3, 1), (3, 2) \}
\]
Each pair represents a point's coordinates on a Cartesian plane.
#### 8) Set of Ordered Pairs 2
This set includes ordered pairs:
\[
\{ (-6, 5), (-3, 8), (-6, 9) \}
\]
These pairs are points that can
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