Horizontal Line Test and One to One Functions

This precalculus video tutorial explains how to determine if a graph has an inverse function using the horizontal line test. If it passes the test, the function is a one to one function.
Introduction to Functions: • Functions - Vertical L...
Evaluating Functions:
• Evaluating Functions -...
Function Operations:
• Function Operations
Increasing and Decreasing Functions:
• Increasing and Decreas...
Relative Maximum & Minimum Values:
• Identifying The Relati...
_____________________________________
Relations and Functions:
• Relations and Function...
Domain and Range From a Graph:
• Domain and Range of a ...
How To Find The Domain of a Function:
• How To Find The Domain...
Average Rate of Change of a Function:
• Average Rate of Change...
The Difference Quotient of a Function:
• Difference Quotient
_____________________________________
Evaluating Piecewise Functions:
• Evaluating Piecewise F...
Graphing Piecewise Functions:
• Graphing Piecewise Fun...
Composite Functions:
• Composite Functions
How To Evaluate Composite Functions:
• How To Evaluate Compos...
Composite Functions - Data Table:
• How To Evaluate Compos...
Comp. of 3 Functions - Data Table:
• Composition of Three F...
Decomposing Functions:
• Decomposing Functions ...
_________________________________
Introduction to Inverse Functions:
• Introduction to Invers...
How To Find The Inverse of a Function:
• How To Find The Invers...
Verifying Inverse Functions:
• Verifying Inverse Func...
Horizontal Line Test - 1 to 1 Functions:
• Horizontal Line Test a...
Vertical Line Test:
• Vertical Line Test
Graphing Inverse Functions:
• Graphing Inverse Funct...
Composite and Inverse Functions:
• Composite Functions an...
__________________________________
Even and Odd Functions:
• Even, Odd, or Neither ...
Transformations of Functions:
• Transformations of Fun...
Linear Functions:
• Linear Functions
Functions and Graphs - Problems:
• Functions and Graphs |...
Functions - Test Review:
• Functions
______________________________________
Final Exams and Video Playlists:
www.video-tutor.net/
Full-Length Videos and Worksheets:
/ collections

[@TheOrganicChemistryTutor]

Next Video: kzbin.info/www/bejne/g6nIY5-OZs2nhM0 Final Exams and Video Playlists: www.video-tutor.net/ Functions and Graphs: kzbin.info/www/bejne/kIWop2uFo6yUrtE Transformations of Functions: kzbin.info/www/bejne/qqq0faNsrZJ6pbc Graphing Polynomial Functions: kzbin.info/www/bejne/qICylpmaprKpqqM

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One to one is Function Many to many is Relation One to many is Relation Many to one is function

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MR. Organic Chemistry Tutor, thank you for solid explanation of the Horizontal Line Test and One to One Functions and its impact on inverse Function.

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Simple enough. Thanks

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[@chillaman35]

Some of those fail the VLT (vertical line test) which would make them not a function at all, correct? (Like the example with the circle)

[@lazylei1797]

I think it only applies when determining inverse function.

[@ajmal_pro07]

Yeahh...if it ain't pass the Vlt...it ain't a function....cuz you'll be getting different outputs for the same input....like...that ain't possible innit ? x=y...same value of x giving different value of y...is not possible..

[@mauricioperez3258]

You should do a surjective injective or neither video

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[@kiramathupallikudam1947]

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[@JeremiahTatola]

what does the phrase "one-to-one" refer to?

[@alexbai3676]

1 x value corresponds to only 1 y value

[@giddynun]

injectivity

[@iidiyalidu1002]

Really simple 10qsss a lot

[@umerfarooq6947]

Hello sir Sinx can't pass the horizontal line test but it inverse exist how

[@a77ackeranimations20]

2:28 Is f(x) in that example even a function? Cause, it looks like it would cross a vertical line twice if it were drawn through it.

[@Prondipan91]

Yes....by definition, it's not a function

[@nevm5776]

@@Prondipan91 your comment is just a month ago, so I have a question, what if the arrows is just a Horizontal line? by using a Horizontal Line Test, will it be One-To-One Function or Not?

[@Prondipan91]

@@nevm5776 If the graph is just a horizontal line, then you can check in two ways: 1. its equation will be y = c (const.). So, its a many-to-one function. 2. if you draw a horizontal line over the existing horizontal line, they will cross each other on infinitely many points. so it fails the horizontal line test. hence, not one-to-one.

[@nevm5776]

@@Prondipan91 ty

[@atharvagunde832]

At 2:50, if a tangent is drawn to a circle, it does have only one place it touches the circle, then what shall we call it ?

[@Wraith_03]

you have to take into account all possibilities

[@abdirizakalihassan2629]

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[@naqeebahmad5897]

thanks man its very useful for me.and i have a question that is inverse function have to follow H.L test?

[@fatal_moon4570]

Naqeeb Ahmad i think the inverse function has to pass the horizontal line and the vertical Line test

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[@dandelion8533]

how about x cubed

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Good

[@Taty-mt7hd]

Does it matter where you place the horizontal line at?

[@a77ackeranimations20]

Well, it does kind of. If the line intersects itself horizontally at any part, it does not pass the horizontal line test. At 3:17 this function intersects at some parts, and also doesn't at some. Since it does at some parts, it does not pass the test

[@dagmawimetaferiya8343]

One to one function, onto function, and one to one correspondence??????please

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how does dis dude got 2.4 million subscribers and has this many views...? im like confused at dis point

[@marien_001]

🇰🇪 Thank you

[@muralimadhav12]

First what is one to one function, I am here for that

[@ayskrim_4251]

Are horizontal lines a one-to-one function or not?

[@rabec_5598]

Horizontal line is not a one to one function... Bcs if we draw horizontal line with it.... It touches infinite of points....

[@ddd-vu7rw]

@@rabec_5598 are they onto?

[@phoenixgre8232]

good job, but isnt f(x) @ 2:53 not even a function

[@nolimit423]

it isnt because it doesnt pass the vertical line test

[@zana2v]

@@nolimit423 then why he called F(x)?

[@babysuyash]

What if the graph passes the horizontal test but fails the vertical test will we have a function or just the inverse ?

[@DARTH-R3VAN]

That's not possible

[@nolimit423]

it wouldn't be a function if it failed the vertical test

[@messagesforscott]

Why does it matter if a function is one to one?

[@vassphire8522]

messagesforscott Because it’s to show whether it has an inverse function or not

[@fatal_moon4570]

Also shows if any x or y values repeat or not

[@ricardoperez2039]

Thank you Mark Wahlberg

[@sharm.a.2677]

You are wrong for a function to be invertible it should be both one to one and onto

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This much easy😲?

[@jackaaronzambrano3774]

Hi alel

[@lorinctelkes1046]

nice content. I got 1 comment tho: you shouldnt draw arrows at the end of every line, only to the end of abscissa and ordinate, because the arrow shows that the values increase in that direction. And it is really bad to draw arrows on functions... sorry, had to say it, it is a fundamental mistake. (i know i know, this is not the point of the lecture but still). cheers.

[@joserulezd00d]

so if it touches the horizontal line test more than once, not a 1-1? yes, i did watch the video, i just like reassurance cus my college exam is tomorrow and i didnt understand this for quite some time..

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[@zana2v]

2:16 bruh this graph is not even a function to called F(x) ?? anyone can help

[@yenvillanueva1501]

It is a function as long as it does not have two points when using the vertical and horizontal test it could be a lot easier if you use the table of value method

[@zana2v]

@@yenvillanueva1501 but it does have 2 points im Talking about the circular graph

[@nolimit423]

@@zana2v it's not a function because it doesn't pass the vertical line test that's all that matters. I'm assuming he's just using random examples to test the horizontal line test and knows it's not a function.

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