Given the following graph, determine if it is a function using the vertical line test, if the inverse is a function using the horizontal line test, and then graph the inverse by choosing points from the graph and flipping the x and y. Function: Original ordered pairs: Inverse ordered pairs: Function: Function: Original ordered pairs: Inverse ordered pairs: Function:

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Question
### Understanding Functions and Their Inverses

#### Instructions
Given the following graphs, determine if each is a function using the vertical line test, if the inverse is a function using the horizontal line test, and then graph the inverse by choosing points from the graph and flipping the x and y coordinates.

### Graph Analysis

#### Graph 1
- **Description**: A straight diagonal line decreasing from left to right.
- **Function**: _______________
- **Vertical Line Test**: Passes (each vertical line intersects the graph at most once).
- **Horizontal Line Test**: Passes (the line is continuous and passes the horizontal line test).
- **Original Ordered Pairs**: _______________
- **Inverse Ordered Pairs**: _______________

#### Graph 2
- **Description**: A vertical line.
- **Function**: _______________
- **Vertical Line Test**: Fails (a vertical line is not a function).
- **Horizontal Line Test**: Not applicable.
- **Original Ordered Pairs**: _______________
- **Inverse Ordered Pairs**: _______________

#### Graph 3
- **Description**: A parabola opening downwards.
- **Function**: _______________
- **Vertical Line Test**: Passes.
- **Horizontal Line Test**: Fails (parabola fails the horizontal line test).
- **Original Ordered Pairs**: _______________
- **Inverse Ordered Pairs**: _______________

#### Graph 4
- **Description**: A horizontal line.
- **Function**: _______________
- **Vertical Line Test**: Passes.
- **Horizontal Line Test**: Fails.
- **Original Ordered Pairs**: _______________
- **Inverse Ordered Pairs**: _______________

### Key Concepts

- **Vertical Line Test**: Determines if a graph is a function. If a vertical line intersects the graph at more than one point, it is not a function.
- **Horizontal Line Test**: Determines if the inverse of a graph is a function. The graph must pass the test to ensure its inverse is also a function.
- **Inverses**: To find the inverse, swap the x and y coordinates of the graph.

This exercise helps in understanding the basic properties of functions and their inverses graphically. Use this knowledge to analyze whether given equations represent functions and whether their inverses are valid functions as well.
Transcribed Image Text:### Understanding Functions and Their Inverses #### Instructions Given the following graphs, determine if each is a function using the vertical line test, if the inverse is a function using the horizontal line test, and then graph the inverse by choosing points from the graph and flipping the x and y coordinates. ### Graph Analysis #### Graph 1 - **Description**: A straight diagonal line decreasing from left to right. - **Function**: _______________ - **Vertical Line Test**: Passes (each vertical line intersects the graph at most once). - **Horizontal Line Test**: Passes (the line is continuous and passes the horizontal line test). - **Original Ordered Pairs**: _______________ - **Inverse Ordered Pairs**: _______________ #### Graph 2 - **Description**: A vertical line. - **Function**: _______________ - **Vertical Line Test**: Fails (a vertical line is not a function). - **Horizontal Line Test**: Not applicable. - **Original Ordered Pairs**: _______________ - **Inverse Ordered Pairs**: _______________ #### Graph 3 - **Description**: A parabola opening downwards. - **Function**: _______________ - **Vertical Line Test**: Passes. - **Horizontal Line Test**: Fails (parabola fails the horizontal line test). - **Original Ordered Pairs**: _______________ - **Inverse Ordered Pairs**: _______________ #### Graph 4 - **Description**: A horizontal line. - **Function**: _______________ - **Vertical Line Test**: Passes. - **Horizontal Line Test**: Fails. - **Original Ordered Pairs**: _______________ - **Inverse Ordered Pairs**: _______________ ### Key Concepts - **Vertical Line Test**: Determines if a graph is a function. If a vertical line intersects the graph at more than one point, it is not a function. - **Horizontal Line Test**: Determines if the inverse of a graph is a function. The graph must pass the test to ensure its inverse is also a function. - **Inverses**: To find the inverse, swap the x and y coordinates of the graph. This exercise helps in understanding the basic properties of functions and their inverses graphically. Use this knowledge to analyze whether given equations represent functions and whether their inverses are valid functions as well.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 4 steps with 3 images

Blurred answer
Similar questions
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,