Visually identifying key characteristics of graphs.

How to identify key features of graphs such as relative maximum and minimum, zeros, domain, range, and y-intercept. We will also state the intervals where the graph is increasing, decreasing, and constant.
Check out www.ProfRobBob.com, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at www.mathplane.com If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage / profrobbob

[@HandleBar3D]

Thank you so much. I am not a student but I love brushing up on math from time to time. I always come back to see your videos for the rusty part of my brain. Having lectured a bit and making videos myself I know the time it takes. Thank you for the hard work and I wish you the best in life. You remind me of the best professors I had in my youth.

[@profrobbob]

You are very welcome and THANK YOU for taking the time to share your story and appreciation and well wishes for the work that I've put into this channel! My wife and I have worked endlessly for 6 years now to keep this channel growing....she answers most of my comments for me since I still teach full-time, don't know what I'd do without her help! Thanks for subbing too, some people don't realize how important that is:( Comments like yours are a constant reminder why we continue to do what we do...BAM!!!

[@kevinhuynh4533]

Thank you so much for taking some time after school to teach students all around the world. You are a true teacher to me because not only that I actually understand the concepts, but I also admire your dedication.

[@profrobbob]

You're welcome and thanks for subbing and supporting my channel and taking the time to share such a nice comment! I do love teaching and it's always nice to hear when it shows thru my teaching:) Please keep spreading the word because that's how we grow and remain free for everyone:D

[@profrobbob]

This was one of my early videos that I taped directly after a full day of teaching...but I get better:) OMgoodness...what's that I hear? You just made me so proud! You are going to DOMINATE pre calc next year with that kind of self-motivation...you're teacher will be lucky to have you!!...and don't let that nasty old "procrastination" invade your thoughts. Take it from experience, "don't put off till tomorrow what you can do today"...

[@ansar4674]

Thank you sir, i am a student from india. During lockdown I wasted my whole time playing PCs And Xbox.. Now when I regreted my negligence And wanted to revise maths. I found you sir.. Thank you sir

[@profrobbob]

Greetings from Florida and thanks for choosing to revise your math skills and chose this channel to study with! Don't forget to like, subscribe and share this channel with EVERYONE...BAM!!!

[@profrobbob]

You're welcome...don't know how your comment got missed, but I apologize...and I hope you are still watching and learning from my videos:)

[@profrobbob]

WOW....now that's a true supporter! I expect to hear about all the great progress you make during the year as a testament to all of your direct links:)...(and hard work)

[@lmafo4utube]

As a transfer student in college I found myself having to build upon the fundamentals of calculus for the placement exam, and these videos have definitely helped me become more solid in math. I now have to get ready for calculus 2. Thank you

[@bigstuff52]

Thank you sir-You clear things up for me that I should have learned fifty years ago. I wish you would have been my teacher back then...........Thank you for doing these great vids for the young people today.

[@Duane_A]

I'm a transfer student also. It's been 2 yrs since I've taken college algebra and your videos are the grade savior (pun intended). I'm in PreCal and have saved your channel as a direct link icon on my iPhone, iPad, and laptop!

[@profrobbob]

Thank you for watching and spreading the word:) Now that this school year is complete I am brushing off my own Caclulus skills and doing videos for that subject. I am glad you like my videos...thank you again.

[@EliWithRob]

Hey thanks this really help me out, it's freshman year and the teachers don't explain well. You made me understand this entire chapter from all your videos thank you very much.

[@profrobbob]

+Robby Elias sorry to hear that:( ...but glad my videos could help you with your chapter studies:) Sounds like a good time to share my channel with all your friends as you remind them to like, subscribe, support the ads and share these free educational channels to help them remain free to help others:D

[@warriorup8622]

Thank you. I totally forgot about realtive max and min. This is a great refresher.

[@profrobbob]

Happy to help…thanks for refreshing:)

[@sofijamarkovic2922]

Thank you so much!! We don't take notes in my math class nor does my teacher teach, this is very helpful

[@profrobbob]

Thanks for taking the time to study:)

[@bllrbob1348]

9 years later and this video is coming in clutch for pre calc

[@profrobbob]

BAM!!! Thanks for watching...please like, sub and share this channel with all your classmates and your teacher too:)

[@georgesadler7830]

Professor RobBob ,thank you for another wonderful explanation of Visually identifying key characteristics /information of graphs. The Ti-83/84 calculators can also be helpful in finding key information about graphs.

[@radhikamutyala3944]

I am really thankful for your videos to help my son is studying IBDP.Your explanation is awesome.

[@profrobbob]

And THANK YOU for being an involved parent and seeking outside help! Please share this channel and support the ads so we may continue to keep growing and helping others for free:D

[@profrobbob]

Just trying to keep you on your toes...Thanks for supporting by watching, liking and subscribing too!

[@ketsune23]

I am a Mec Engineering student freshman and I totally flunked on Calculus starting my marathon with you professor RobBobn :) hope to get a A+ next semester ;)

[@profrobbob]

With a lot of hard work I am sure you are going to pass Calculus with that A+!!! Here is my Calculus playlist organized by chapter and topic, www.profrobbob.com/calculus

[@profrobbob]

Write your answers consistent with what your book and teacher shows. In my PreCalculus book the intervals are shown with ( non-inclusive brackets) because the function at those exact values like at 2 has a horizontal tangent line indicating the slope is 0 at 2. The slope is negative at 1.999..... and positive at 2.0001 but 0 at two.

[@profrobbob]

That is GREAT:) Thank you. I hope you do fantastic in Calc 2! I wish I was far enough in building my math channel to still be of some help in your new class.

[@7median]

You almost killed me with that BANG! at the end ..... but seriously that was really helpful, Thank you.

[@xzayviyo]

Thanks any time I need help I turn to your channels. my tutors at times just tell me the answers and don't ensure that I understand thanks u rock. I may finish my bachelor's bc of u.

[@profrobbob]

+Carrie G that's awesome! (maybe some of the tutors should watch:) We appreciate the support and can't wait to hear about graduation day:) Thanks for studying with Tarrou's Chalk Talk and for liking and subbing too...I hope you are telling all your classmates to watch and do the same:D

[@superking9559]

Thank you! Thank you so much for these videos! You explain these topics really well, and way better than my professor!

[@profrobbob]

You're welcome Nikola Mitevski Thanks for watching and you can help me by liking, SUBSCRIBING and telling your friends, classmates and teachers to watch and use these videos as an additional study reference then to SUBSCRIBE and "keep sharing" to help these free educational channels grow and remain free!

[@superking9559]

No problem! Yeah, just keep up the great work and I'll tell others about it! Also, do you plan on expanding the amount of subjects that you teach? It'd be great if you covered Physics as well! Of course, if you have time haha.

[@profrobbob]

Nikola Mitevski THANKS! No plans on a Physics play list:( I'm currently working on adding to the Algebra playlist then it will be Calc2 but full time teaching keeps me much too busy these days for either...so I just do what I can, when I can, and hope students keep watching and sharing like you are! Thanks again :D

[@mersenne2486]

thanks for these great lectures

[@profrobbob]

You are very welcome! Thank you for watching ♥️

[@java4235]

I want to give you a thumbs up on your teaching style!

[@profrobbob]

THANKS!...what about the other two?!...lol

[@arshia643]

At 4:01, wouldn't you use a ] after the -1 and before the 2?

[@Bheilla]

Great explanation! Thank u.

[@profrobbob]

...and thanks for watching!

[@stevenoverton8316]

You never disappoint.

[@profrobbob]

Thanks for the sub, the continued support and the positive compliment!

[@margieschneider1819]

All I keep seeing is Castiel from Supernatural. These videos are awesome! I'm learning so much. Thank you!!!

[@profrobbob]

margie schneider thanks for the compliments...sure beats looking like Mr Bean!!! Thanks for watching, learning and subbing too!

[@GreaterDeity]

Wow, you're right. Just now realizing how much he looks like Castiel. lol

[@WarDonbloopu]

Holy shit. Keep it up! You explaining small things like the use of the bracket "]" helps so much.

[@profrobbob]

Thanks for watching...please sub and share this free math channel with everyone as you remind them how important it is to sub and share ALL the free channels that help you:)

[@roundearthshill247]

Wow, I actually get what this is about, thank you! Subbed and Liked

[@profrobbob]

+alan scott BAM!!!

[@profrobbob]

Welcome to Tarrou's Chalk Talk and THANK YOU for liking and subscribing all the way from India! I miss the old KZbin format that showed where subscribers were from:( I hope you continue to enjoy your learning experience and if so please share with your friends at school...and best of luck with your studies!

[@profrobbob]

Thank you Thank you Thank you:) I wish there was this kind of help too when I was in school:)

[@profrobbob]

The graph starts to rise from its minimum of -2, but I am identifying where along the x axis the graph is increasing...and it starts to increase at the x value of 2. Thank you for the kind words I really appreciate the positive feedback. I hope you do great in your college algebra class.

[@MaLeVoLeNt7319]

Hey professor quick question I noticed that you used open parentheses on - 1 and 2 in my textbook they use closed brackets unless their is a hole on that point, your thoughts? Love the videos btw

[@profrobbob]

Some books define increasing and decreasing on an open interval, that is notation I am using, while other books define increasing and decreasing on a closed interval which is the brackets you are seeing. Just be consistent with your book and teacher:) Thank you for watching and your kind words!

[@i_harib]

Hi Sir! First of All i want to thank you for these wonderful tutorials. Sir, i have a question in the above graph it has another maximum value at x=6 now what i m asking is that is it another relative max or we'll call that an absolute maximum??? Please reply if possible :) Thanks again

[@gjironman13]

Enjoyable Mr. T, hope you're feeling better. Glen

[@profrobbob]

Thanks Glen! Went to the Doctor monday, have bronchitis, prescribed z-pack, went to fill prescription...noticed someone sideswiped my car and left no note:( Talk about feeling BAD!!!

[@gjironman13]

ouch!

[@ziksimon4136]

Do you always say bam! at the end of your videos because you 'killed' it?🤣

[@profrobbob]

Yep! I love teaching math, what can I say. Whether I "killed it" can only be determined by you🙂 If so, please hit the like button and share with your friends. I have around 670 more math videos organized by subject and chapter at www.profrobbob.com BAM💥

[@06100423188]

In the increasing and decreasing areas, would -1, 2, 6, -1, and 2 be inclusive in the interval notation? Because I learned it as using a bracket "[" for inclusive numbers.

[@06100423188]

At 4:00, would 2 be inclusive in the interval notation? Because I learned it as using a bracket "[" for inclusive numbers.

[@profrobbob]

I'm not trying to kill anyone, just going out with a BAM!!!....lol If you continue to watch, be prepared that word gets used a lot:)...thanks for watching.

[@gdfauxtrot]

When answering graph directions ("Where is the graph decreasing/increasing/constant/etc."), would you advise explicitly mentioning the 'x' before your answer? (ex. "x=(-inf, -1)" instead of just saying "(-inf, -1)") Or, does everyone pretty much read graphs left to right and would understand your answer anyway?

[@profrobbob]

G. T. Duarte You need to read the graph left to right and interval notation should always have the minimum value first. Putting the x= in front of the interval notation is just something I like to do to continually remind my students that we are talking about movement along the x axis.

[@profrobbob]

@Shorty20122012 Thank goodness I was actually pointing at -1 when I said the wrong number! :D

[@mdtamimmahamud7258]

Connectivity is at the heart of Facebook's I d shathi tamim

[@shubhkarmanjitkaur4988]

What if there are multiple rises and falls in a graph, then what will be the relative maximum and minimum?

[@ami-lu3ud]

great video, you just saved my grade on my quiz :)

[@profrobbob]

I'd call that teamwork:) YOU saved your grade by seeking outside help + I helped with my videos = teamwork...BAM!!!

[@aeroz2804]

Very good explaining.

[@profrobbob]

Thanks for watching!

[@faithm6732]

I would totally like you as a teacher

[@profrobbob]

Just like and subscribe and I'll be your KZbin teacher:)

[@america2695]

BAM! love it

[@profrobbob]

...and I love that you are watching more videos!

[@steelpanther88]

I have a silly question from 05:20 onward. You said that the graph is increasing at interval (-infty, -1) and decreasing at interval (-1, 2). Is it incorrect to assume that exactly at the singular point (×=-1, y=4) the graph is constant at that single point? Or is it wrong to say single point has any particular direction increasing or decreasing or constant.

[@profrobbob]

@thomasjrbg Thank you:)

[@gracenguyen5870]

why is the constant (6, infinity) when the x-axis is what is changing, not the y-axis?

[@sighisoaraa]

When finding relative maxima and minima, don't you need to specify the domain?

[@shaunavidaurri7625]

On the 4:00 mark, wouldn't the second increasing point start at -2? BTW your videos are great! I used them last semester in my Intermediate Algebra w/ Review and I am using them again in my College Algebra class. (math is NOT my best subject.) :) THank you for all the helpful videos!!!

[@leisurelion4702]

saved my life

[@sarahkhan9549]

thanks alot ! thumbs up

[@profrobbob]

+Sarah Khan you're welcome...please like and sub too:)

[@Nriab321]

"AND BEYOND" that woke me up Lmfao thanks for the aweswome helpful videos !

[@ajfisher2140]

thx for the help i passed my test

[@profrobbob]

thanks for studying...please like, sub and keep sharing:D

[@14sabz]

...and it goes to infinity.... AND BEYOND!! XD my fave part lol!

[@profrobbob]

Keep watching now that you have subscribed and I'm sure you will continue to be educated and entertained:) Thanks for choosing Tarrou's Chalk Talk to learn from!

[@14sabz]

I am really glad I found you. Just started my first year at university and my Calculus 1 lecturer isn't the best at explaining. So thank u A LOT!

[@profrobbob]

14sabz Me too...then please be sure to share my channel info with your class too:)

[@jainilshah7103]

I mean so the x-int is the same as saying the root, zero or solution??

[@profrobbob]

Correct!

[@DopeBoysClan]

no big deal, my friend, but at the end when you add an asymptotic of 5, your inequality sign must have the (or equal to) removed from the less than 5. Nonetheless, wonderful videos, there are not enough space in the universe to fill my thank-yous that would express my gratitude.

[@profrobbob]

Thank you. I made an annotation correction to the last few seconds of my lesson:) Your kind words and support are greatly appreciated.

[@profrobbob]

To infinity...AND BEYOND!!!

[@TheRaphaim]

Did you go to uvsc or hsu you seem familiar.

[@profrobbob]

Nope...USF...must just have that "familiar face" James Busald

[@profrobbob]

+Rorschach 12 yes, Tampa Bay...lol...Florida! Almost the same temps...thanks for studying and subbing to this channel...please tell all your classmates to watch and do the same:D

[@GreaterDeity]

Chabot College?

[@antoniojemcatubig6703]

could please help me at my math special project please

[@DivineYT]

6:41 "saying that your relative maximum of 4 is occurring at the x value of -2" LOL

[@kingcalebgabriel4695]

Lol I accidentally clicked the pause button when he said "and beyond!" dat face tho lol

[@profrobbob]

Thanks for studying and subbing and paying attention...BAM!!!

[@steelpanther88]

why do you say that the graph increases in the first interval OR the second interval? What does the U-notation mean in this graph example, with the intervals? why aren't BOTH intervals active, at the same time? Why OR, instead of AND. Why is it EITHER the first, OR the second interval? Clearly the graph is increasing, in BOTH intervals, so clearly both intervals are active, so to speak? Maybe I'm not following your point. This U- notation was seldom used in our class. In high school we used the x greater or lesser than- notation.

[@profrobbob]

U means OR, yet like you I want to say the function is increasing on both intervals...because it is...but I cannot use the "and" symbol. U upside down. If shading compound inequalities on a number line, "or" includes all the shaded area and for "and" you shade the overlapped area. There is no overlap in the intervals of (-infinity,-1) and (2,6) and thus if I said "and" you would in a way be saying there was no solution.

[@steelpanther88]

ProfRobBob thanks professor Rob, I misunderstood the meaning of the U-notation. My misunderstanding was a combination of your spoken word "or", and misunderstanding of the specificness of the U-notation. When spoken in any given sentence without further explanation, "or", can have the following meaning "either this, or that". At least, that is sometimes the meaning, especially when talking to people sometimes. In other words, in English, there can be an implied meaning of choosing out of necessity, "either A, or B." In our high school, we only used the notation "X greater or lesser than". To me, this latter notation, always felt more comfortable.

[@mmukulkhedekar4752]

where's the BAM

[@profrobbob]

Nice catch...this was one of my earliest videos before I implemented the BAM!!!...lol

[@ghostfrom1950]

uhhh... at @ 11:34 ?

[@musicaldisaster1141]

omg he looks like castiel the world is ending

[@profrobbob]

Please sub and share that castiel is teaching math...BAM!!!

[@Andy-ek5by]

I like your username xD

[@profrobbob]

+Andy Rendas BAM!!!

[@Jabermania]

to infinity and beyond 😂😃

[@profrobbob]

+Jaber Al Marri BAM!!!

[@jacoblagasse6763]

BAM

[@profrobbob]

...that's what I'll say after you subbed share:)

[@thickachu4001]

Aw no BAM!!

[@Death_User666]

gangsta

[@parenthope3]

I think your shirt is improper

[@profrobbob]

You just brought a smile to my face. Your comment tells me you have been doing your homework:D

[@parenthope3]

I've been an Algebra teacher for over 12 years. I'm working on my own Algebra I class.

[@profrobbob]

That's awesome...I just started my 21st year. It's always nice hearing from a fellow teacher:) Please take the time to share this free channel with all the rest of the teachers at your school and remind them all to like, subscribe, support the ads and keep sharing all the free educational channels on KZbin, that's how we continue to grow and remain free for everyone:D