INTALG 2.2: Graphs of Functions

We review graphs of functions. First we show how a function gives a graph in the xy-plane. Then we give give the Vertical Line Test, which determines when a graph in the plane represents a function. Then we show how to extract data from a graph of a function, and how to find the domain and range.

[ruinenlust_]

I just watched a video of yours from 10 years ago, and very (happily) surprised to see you still going!! You're an absolute legend

[vanessagarcez]

Hi Bob! I hope you are healthy and safe! You helped me a lot when I was an undergraduate! (about 2010's)
We love you and your channel :)

[trendingduniya]

I am student from IIT and taking your lectures which was uploaded 12 years ago and then i saw this video and realize how fast time changes and that gives me nostalgic vibes and I am also happy too see you passionate about math's you are good tech.

[ranglovesyou]

Thank you so much for everything dr bob!! I saw your videos from 10 years ago and they help a lot, keep going, your hard work isnt going unnoticed !

[archeryrangesonaneutralis]

Please continue your algebraic geometry series it's good

[dommywommey]

Your videos were amazing. I feel like any time I have been confused about something I come to your videos and it clears everything up! Im taking abstract algebra as of now and a lot of your videos have helped me tremendously. I hope everything is well with you! Thank you

[lluzard]

Wow! I am glad to watch this! He came back!

[actuallycarl]

Just came here from a Maclaurin series vid. You are awesome man, completely saved my Calc 3 grade

[arnabrahman]

​ @MathDoctorBob Please make more videos, your videos are so easy to understand. Your calculus ones are amazing and have definitely saved my grade, many thanks!

[harshg-hm]

Sir i just watched you 11yr old video of LT, and your teaching style is still same and amazing🤩, just the stick changed 😄,

[freakhead]

You got me through a lot of engineering school math. Thank you so much.

[studytimebyfoziabarlas]

Great and easy way of teaching. Thank you.

[RexGalilae]

Boy, I just came back to this channel after 5 years, probably and you've changed so much in appearance lol.

Seems you've lost gained a few pounds and have aged a bit haha

[edwardjtorres]

How can we support your work? These videos are GOLD!😀

[nathanhawey]

Have you got year 1 university maths.Or would you recommend me anyone because I want to self teach.

[thurqs]

hello bob! i wish you are still healthy and happy man!

[SuperYoonHo]

Subscribed but do hard olympiad maths plz

[mansoorwahab]

How did Dr. Bob age this much in a span of 10 years? Did he get married?