Which equation is a function and why? ### Educational Website Content: Graphs and Diagrams#### 1) Linear Function GraphThis 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 GraphThis 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 GraphThis 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 FunctionThis table shows the relationship between x and y values:```x | y----1 | 12 | 13 | 1```Here, for any input $ x $, the output $ y $ is always 1.#### 5) Function Mapping DiagramThis 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 FunctionAnother table indicates the relationship between x and y values:```x | y----1 | 32 | 43 | 6```Here, the output $ y $ increases as the input $ x $ increases.#### 7) Set of Ordered Pairs 1This 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 2This set includes ordered pairs:\[\{ (-6, 5), (-3, 8), (-6, 9) \}\]These pairs are points that can

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1) 2) 3) -3-2-18 O 2

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

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

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