Horizontal Line Test and One to One Functions  Summary and Q&A
TL;DR
This video explains how to determine if a function has an inverse function by using the horizontal line test.
Key Insights
 A function must pass the horizontal line test to have an inverse function.
 Onetoone functions have inverse functions, while functions that intersect a horizontal line multiple times do not.
 Parabolic functions and those that intersect a horizontal line at three or more points do not have inverse functions.
Transcript
consider this function let's use a linear function as our example and let's call it f of x so does f of x have an inverse function determine if f of x have an inverse function you have to show that it's a onetoone function you have to show that it passes the horizontal line test so if we draw a horizontal line that's a terrible horizontal line if... Read More
Questions & Answers
Q: What is the significance of a function passing the horizontal line test?
If a function passes the horizontal line test, it means that it is a onetoone function, allowing for the existence of an inverse function.
Q: How can we determine if a function has an inverse function?
By analyzing whether the function intersects a horizontal line more than once, if it does, it is not a onetoone function, and it does not have an inverse function.
Q: Can you provide an example of a function that has an inverse function?
Yes, a linear function is an example of a function that has an inverse function. It passes the horizontal line test as it intersects the horizontal line at only one point.
Q: How does the number of intersection points with a horizontal line affect the existence of an inverse function?
If a function intersects a horizontal line at multiple points, it implies that the function is not onetoone, and therefore, it does not have an inverse function.
Summary & Key Takeaways

To determine if a function has an inverse function, it should pass the horizontal line test and be a onetoone function.

If a function intersects a horizontal line more than once, it is not a onetoone function and does not have an inverse function.

Examples of functions that do and do not have inverse functions are provided, demonstrating the application of the horizontal line test.