How to Evaluate Functions (Precalculus - College Algebra 3)

How to evaluate functions of both constants and other functions (composition of functions). Also discussed is the Difference Quotient and it's use.

[horizonbrave]

"Can you take zero slices?" "Yea it's called a diet, you don't eat the pizza".... My god Leonard you have so many classic lines..

[RStell-wtqr]

I've never contributed to anyone's patreon, I'm very poor. But I'm willing to sacrifice a meal or two to support this kind of content.

[arsdwalos]

You quickly became my teacher that I never had. Thank you from my bottom of my heart

[jacobrzeszewski]

YouTube is such a valuable tool for my learning. I have ADHD and being able to rewind back to go over a section I blanked on or missed is so useful.

[me-tubemath]

Today is teacher's day in india.
Mr. Leonard your teaching style is great.
Prealgebra
Intermediate algebra
Cal: 1, 2, 3
TTP VIDEO
Differential eq.
...all are very helpful my life.
HAPPY TEACHER'S DAY mr. leonard.

[PaquiCamus]

I have just subscribed to your channel. I am a retired scientist(hydrogeochemical), a chemistry degree of about 50 years ago. I did calculus and algebra but have used just a little. Now, I have to help my grandkids to get into University and they want to be engineers and scientists. No problem to help them in chemistry and physics but Advanced Maths to prepare them for Calculus is a great pain. I have been avoiding it until now. Universities in Australia have Advance Maths plus Extension as a pre-requisite. Consequently, I have no choice but to review pre-calculus and calculus. So far I have really enjoyed your presentations and advice: "Do not do in your head but worked out in the paper" Great advice! I like the way you teach and present the topics. I am catching up and teaching my grandson for his preparation. Thank you very much, Professor Leonard. Still have 3 granddaughters and 2 grandsons waiting their turn.

[Rainsong]

May the Lord bless and keep you for helping so many students across the globe to ENJOY Mathematics again !!!
:D
The world needs more teachers like you, who actually teach in a way that doesn't BORE students, and also...
you don't speak in a way that "looks down" on the students !

All of us here on YouTube appreciate your effort and good work !

[zachallen]

You have had impacted my life in the best way. I thought I disliked math, and avoided degrees that required it. Now I am getting the chance to give it another shot, and I have never felt more confident. I have also never had such a great teacher.

[daviandrade]

When you realize you're watching professor Leonard's videos like you would watch friends, that is, just for fun. Best professor ever!!

[DirewolfMemento]

For those confused as to why (x+1)^2 = x^2 + 2x + 1

Here is why it is since he brushed past it a bit.

the expression (x+1)^2 = (x+1)(x+1) meaning (x + 1) times itself.

Which means you would take (x)(x) and get x^2
and (x)(1) = x
and (1)(x) = x
then (1)(1) = 1
If you simplify you would combine x + x which equals 2x
Then your answer would become x^2 + 2x + 1

[douglasgorney]

I never ever ever got this stuff in junior high and high school, and when it came to college, I didn't even try. Wish I'd had you as a teacher then; it might have gotten through my thick skull.

Have always felt incomplete regarding math, so I'm finally going back with the intention of getting to and through calculus. Thanks so much for the help!

[ernieparchment]

Thank you professor. I am taking pre calculus after being out of school for over 20 years. You make learning math easy and enjoyable and I can see your love of teaching. Best professor ever😊

[jackie]

At 31:15- Best explanation of dividing by zero I’ve ever heard. I needed this in grade school. Lol .

[MariniaGroup]

This is probably the best math instruction I have seen on this topic. Excellent teaching.

[GammaFields]

Thank you, Professor! This is roughly where I left off in HS almost 8 years ago. Watching these has been the perfect refresher to prepare me for my transfer degree at my C.C in April. I've been bouncing around between different lectures, and yours is the one that's really made it click/set in. You've given me many "ah-ha!" moments, and Im looking forward to working through the rest of your video series to further prepare myself.

[krystinkaminski]

I would have never have made it through any of my math classes without you! Its because of you I was able to teach myself all the way through statistics and skip 4 semesters of math. Your the best and I recommend your videos to anyone learning math. Everyone who took my advice all agreed that you are amazing. I wish you taught financial accounting and investment analysis too!

[dayanaracastaneda]

Professor Leonard you are truly a life saver, and one of the best professors I’ve ever encountered. My college professor currently always manages to make simple concepts complex and you make everything easy. Thank you very much.

[hjkjy]

This made me think that i'm probably not hopeless in math, thank you so much Prof Leonard!

[MathswithMuneer]

You are doing a wonderful job and you inspired millions, that is why young teachers like men are also in this profession. Together we will make world without fear of math.

[ehab]

I recently transferred universities and lost my math credit and as a junior this is the hardest class that I'm currently taking but these videos have such clear cut examples and explanations that it honestly dissolved all my worry, thank you for making these videos and they will definitely assist me this semester