Difference Quotient

PreCalculus introduction to the Definition of the Difference Quotient

[ItsPouring]

I have wanted to say a HUGE "THANK YOU" to you Professor RobBob for your generosity in posting such GREAT math tutorials. You do it in a very clear and organized manner. Not only are your students benefiting from your clarity and organized presentation of often confusing concepts, but the ENTIRE online community benefits as well - that's GENEROSITY!! Thank you so much for your excellent math tutorials!! ❤ "BAAAMM!!" - now I'm gonna go do my homework 😄

[BerryBeastinU]

I swear this guy explained to me in 15 minutes, what my teacher couldn't do in a 2 hour study session, thank you ProfRobBob.

[profrobbob]

WOW...thank you again for such a wonderful review. I really do appreciate all the support from my subscribers, doing these videos after a full day of teaching is very time consuming (just ask my wife) but the end goal, and the uplifting comments make it easy to continue. With the help of people like you spreading the word...my channel will continue to grow bigger and bigger and help others whom might not otherwise be able to get extra help...thank you for being a part of my quest!

[profrobbob]

If f(x)=2x-1, then f(x+h) is telling you to replace any x in the function with x+h, thus you have 2(x+h)-1. Thank you for choosing my video and I hope this clears up you question.

[mattduran]

When I took college algebra this is one of the first things my professor taught us. He was a good professor but did not explain the origin of where the h comes from, thanks for explaining

[xxenxx]

nanananana dont know what id do without you. Thanks so much, I was so lost but now I found this.

[profrobbob]

Thank you for the nice feedback. When you want to evaluate/simplify f(x+h) write out the function with empty parentheses where there is an x, and then go back and put x+h in each of those ( ) and simplify. When the difference quotient asks for f(x)...well that is just the original function that was given so just write out the function. When you write out f(x), don't forget to wrap it parentheses because you need to distribute the - sign through that function.

[profrobbob]

And thank you for subscribing and working so hard over the summer:) You keep watching and I'll keep answering those comments the best I can:D

[coltwyndham]

This is one of the few videos that explains the IDEA behind the DQ and what it means, and that’s very helpful. Thank you!

[AB-pies]

God bless you sir! I was struggling with this and you really explained it well. Not only did you show how to work it. You explained the background so it sticks!!!! Thank you much!!! Found this Feb 2019

[profrobbob]

Happy to help from so far away!...You're welcome and thank you for watching:)

[TotsFabulous]

Thank you so much. Just went over how to simplify this formula in my pre calc class, and it kills me when I don't know where something comes from. Great explanation.

[profrobbob]

You're welcome. Happy that I could help!...now you can help me by subscribing and sharing my channel with your friends:D
I will keep making videos as long as you keep watching and learning!

[profrobbob]

You are so welcome...I'm glad to hear that you are un-stuck now:)...and thanks for watching and subscribing!

[emil]

ProfRobBob, you're a really great person for this. Talk about giving back to the community. You make everything so easy to understand. Thank you very much for taking the time to make these videos.

[Brocephus]

Sat through class. Went to my professor's office hours. Stared at my homework for twenty minutes. Watched this video. NOW I get it. Thanks for helping me to understand that this difference quotient isn't the monster it looks like. It really is quite simple when you understand both the "how" and "why." Many thanks for taking time from your own day, to make my time worth a little more.

[striver]

You are an Excellent Teacher!! So clear and precise. I'm so glad I found your channel. I am in PreCal and can't afford a tutor. You made all the difference!

[Alexa]

I've had three separate professors try to teach me this over two years, and this video finally made me get one correct. Thank you.

[vmax-hd]

Cant say thank you enough, there need to be more teachers like you in this world

[Love-Within]

you make math seem much more simple and actually treat your audience like they are intelligent people, VERY great! keep them up!