Support: / professorleonard Cool Mathy Merch: professor-leonard.myshopify.com/ A study of the library of functions used to do transformations. Key points, Increasing/Decreasing, Domain, and Range, Even/Odd included.
I'm in calculus 3 and this video is still VERY relevant. I never learned (or was even taught) any of this in the TWO PreCalc classes I took and it really came back to bite me during Calc 1 and 2. Thanks, Professor!
I am now in my junior year in electrical engineering but I still watch your videos to keep me fresh. You are a gentleman and a scholar, truly. Thank you so much.
when I finish college I will be owing those youtube supermen and superwomen a lot! you saved me in high school and you are saving me again right now. I wish you get what want in life just like you allowed us to get what we wish by these videos
*Handy tip:* The curve on the graph will bend one time less than the exponent in the function. x^1: Doesn't bend at all. Straight line. x^2: Bends once. x^3: Bends twice. x^4: Bends three times. x^5: Bends four times. And so on.... :)
Professor Leonard, this lecture analyzes the graphs that all students in science and engineering students should know. Students should have a deep understanding of these graphs and their impact in mathematics.
I’ve been very appreciative how much work you put into this. I’m review my pre calc before this fall semester. I have calc 3 and Modern diff eqs. Kinda crazy haha thank you once again
Using all the best, positive and wonderful from the dictionary won't be enough, I can just say that I'am and will be grateful for ever. Thank you Professor Leonard, may GOD bless you and all that you love and care about.
Thank you for actually explaining why the graphs are shaped the way that they are. This was not explained to me while taking college algebra. Now I am better prepared for calculus.
In INDIA we call Guru to a teacher, We touch their feet to give respect. Every time I see your video It simply comes from my heart to touch your feet. That has never happened to me throughout my life. You are simply amazing. I had a feer of Mathematics. Now it's gone. Thank you.
DEAR PROFESSOR LEONARD, YOUR VIDEOS HAVE HELPED ME GET THROUGH HIGH SCHOOL AND COLLEGE. I’VE JUST STARTED LINEAR ALGEBRA AND I’M STRUGGLING GREATLY. THE TEXTBOOK IS ASKING ME ABOUT QUESTIONS THAT IT DIDN’T EVEN DO ANY SAMPLE QUESTIONS ON. PLEASE DO A SERIES ON.. INTRO TO SYSTEM OF LINEAR EQUATIONS. I NEED HELP WITH FINDING SOLUTION SET OF EQUATION(S) WITH MULTI-VARIABLE EQUATIONS SUCH AS ** x - 2y + 3z = 5** etc
I failed in Math(Calculus) in college because I took different field not related in STEM when I was in middle school. Now I'm here to finish all this course to fight back and pass that Calculus subject. Next I would take the Calculus course together with some textbook that I found in the internet.
Love your video Professor Leonard! You have helped me a lot this semester. Next semester I will be taking Elementary Calculus. What serious would be best for me to study before going in to it?
I’m really getting into your videos to make custom indicators for forecasting in the stock market and I gotta say you look just like me man we could have been clones you’re probably about 10 years older than me I’m 25 I wish I would have taken math more seriously
I can't remember shapes of graphs. I can remember what defines the shapes. All but 2 of the graphs are variations of f(x)=x. f(x)=|x| is a piecewise function where y for -x is inverted. Most of the rest are described by the exponents of x. Square and cube roots are fractional exponents. The farther the exponent is from 1, the sharper the curve of the graph at its apex giving a more squared off line. The larger the exponent, the more the apex of the curve will move away from (1,1) toward the x axis making the line more vertical. The smaller the fractional exponent, the more the apex of the curve will move away from (1,1) toward the y axis making the line more horizontal. For function with x as the denominator, y is the reciprocal of x. I would love to see a video showing this and tying in transformations as a way to further tweak the line that exponents or a fraction created.
1/x still fit -f(x) = f(-x) yet i said its not odd because it doesn't go through the origin, so which is it? does odd function need to cross the y-axis as while to be odd?
it does not need to be go through the origin instead its has to be symmetric of the origin. Anyways, in other way we can prove that f(x) = 1/ x is odd function, f(-x) = 1/(-x) = -1/x = -f(x) so its odd function
*Handy tip:* The curve on the graph will bend one time less than the exponent in the function. x^1: Doesn't bend at all. Straight line. x^2: Bends once. x^3: Bends twice. x^4: Bends three times. x^5: Bends four times. And so on.... :)
