CONGRATS Morgan...that's a big step to take! You're welcome and thanks for taking the time to like, sub and thank the teacher already:) Please take every opportunity to share this free resource with everyone, especially classmates and teachers so we can remain free and continue to grow and help others...BAM!!!
Thanks for studying with Tarrou's Chalk Talk...please return the help by taking the time to like, sub and share this free educational channel with everyone:D
Ok I know Im suppose to be focused on math, BUT...every video that ProfRobBob does I always find myself saying, "Wow...I love his handwriting!" GREAT videos! Thank you!!!!
Video 19 in my slowly growing Calculus playlist. Look for Instantaneous Velocity and Speed of Linear Motion. It is a full lesson where I compare average velocity to instantaneous velocity and discuss the difference between velocity and speed.
You're a great teacher! And you helped me pass this week's homework! I don't leave comments, but I had to this time to show how appreciative I am. I especially REALLY liked that you explained the slope in the second problem. It really helped to understand the problem even more. Thank you. Don't stop making videos! I know I am going to need it for next week too. lol. Have a good weekend. BAM!
Thanks for choosing #ProfRobBob to watch and learn from GOREjess7 and taking the time to comment and thank the teacher! I hope you will take the time to help us groW by liking, subbing, supporting the ads and telling others to watch and do the same:D After you sub, you'll be able to find me all the time whenever you need that extra little bit of help the next time...BAM!!!
:D...that's me laughing out loud at your reply! You sound just like one of my favorite classroom students...lol Makes me proud to be your "teacher" too!!! Just for that, I'm going to work even harder at trying to master the dash and will feature it on a video...and when I do, I will dedicate that video to you Hayden...(and will let you know where to find it:)
Thanks for tuning in...glad to hear you like my channel! Please take the time to sub and share this free resource with everyone...BAM!!! (especially your teacher:)
In calculus, the concept of derivitives, you will learn how to find the slope of a curve line at a given point...or value of X. Hence, you will find that slope varies with x along a curve. Outside of derivitives, slope is a constant rate of change defined as "change in y per one unit of change in x." So to answer your question here...no...slope is not ax+b.
Thanks for choosing to watch my lesson. I hope you do great in your class. I have an organized list of lessons here for more help. And please help by spreading the word about my free math lessons:) www.profrobbob.com/algebra-2 or www.profrobbob.com/pre-calculus
And THANK YOU for seeking additional help and choosing my channel to learn from. I'm totally humbled to even have Kahn used as a comparison from you:) I hope you will keep me in mind if you ever need more help or just as an alternate learning channel! Please share your discovery with your friends too...my wife and I are working very hard to groW my channel and spread the word:D
Professor RobBob ,thank you for a solid analysis on the Average Rate of Change and also the true definition of a Slope. Average rate of change is also covered in Calculus One.
THANK YOU! I love teaching and sharing my passion with students who are willing to take that extra step and get outside help...thanks for being one:) Don't forget to spread the word:D
Thank you so very much for all the support! I really appreciate all the "likes" on your channel page and thank you too for subscribing:) Please spread the word to your friends too:D
Thanks for watching, learning and subbing Dilnaz Afghan ! Glad it helped:) Please share my channel with the rest of your class and please remind them to like and sub and support the ads to help us keep growing:D
Hi Mr. Tarrou, it was just today, while reviewing some PreCalculus that I realized I needed to clarify "average rate of change". Of course, it is not a difficult concept (if you already understand slope of a line), but this is still a useful lesson. I just made a small donation to acknowledge the contrbution you have made to my education.
Even in summer you have to make sure you know what you're doing for next year x) I'm starting advanced pre-cal as a junior and your videos are a big help. Thank you so much for posting them and keep doing what you do:) -Emily in Texas
For once in my life I feel like I can actually understand math again. I'm currently taking Pre-Calculus/Algebra 3 with trigonometry and this is my final year of high school, and I'm very happy to say that I'm definitely gonna subscribe to your channel so I can be able to pass this class AND be able to understand what I've learn when I'm out of high school. I'm glad your channel exists Prof. Rob Bob :D
+Fairy T. and I'm happy to hear that you have found this channel so helpful! Thanks for investing in your education and taking the time to study and find outside help and for choosing my channel to learn from and support:) We also thank you for taking the time to share your appreciation and wish you all the best in the future.
you are such a great teacher! I prefer hearing you over my think cuban-accented teacher LOL thanks again for taking time to teach alot of confused kids!
Thank u so much! I subscribed because u do such helpful explanation in this video and in every video you do. And I'm 100% you explain better than my 8th grade teacher. I just wish I was in your class than in her class right now.
Thanks for seeking outside help and choosing this channel to study from...sounds like a good time to share my channel with your teacher so all the rest of the students who want to study at home will know where to find this free study help and you could also get a group of classmates and watch the videos and work on homework together...it's the next best thing to being there...BAM!!!
11:16 What if you had to determine the average rate of change, between 70mph and 20mph. In other words car is decelerating from 70mph to 20mph. Obviously speed of a car, cannot be negative, because speed of a car, is not a vector quantity ; speed only has magnitude. But at the same time, All cars can decelerate or accelerate, or travel at constant speed. This is proven fact, indeed! Would you calculate the problem in the same way, in case of a decelerating car?
Thank you for this video! I have been using Khann Academy, but the videos for average rate of change are awful. This was explained clearly and in an understandable way. Thanks!
I have been studying it, and it looks like the distance between the dashes is proportional to the speed of his arm. Which leads me to think it is how he is holding the chalk that makes it work. I don't have a chalk board to test my theory on, but I think he may be holding it loosely between his fingers with it aimed against the direction of travel so it jumps as he goes. hahaha I just really think you can do this Mr Tarrou! Thank you for replying, hope your doing well! Hayden
Look at you watching more videos, now that's AWESOME hearing the words love and math in the same sentence!...I just sent you a long reply to your flattering last comment:) Please share your experiences with your friends and classmates and someday maybe we will have that "M" next to my subscriber count!!!!
You know this graph actually helps me understand now what domain and range really is. in this mpg sample the domain or x is the speed, and it's being compared to mpg which is the range. technically speaking the speed could be infinity just like the domain in sin cos tan but the mpg is only limited between a max n min y value, you can only get so many mpg that can't be infinity so that's why it's the y axis or the range. bam! did i get that right? thanks again for all your help!
Hey Prof. Rob Bob, I just subscribed! I am taking pre calculus in college and just watched the average rate of change video. My suggestion would be to go on with the secant line. I looked to see if there was another video for secant line, and there wasn't, at least I couldn't find one.
Kim Heisel The slope of the secant line is the average rate of change and the slope of a tangent line is the instantaneous rate of change, but you will not see that until Calculus. I compare and discuss this in a couple of my Calc videos. I should have used the Secant vocabulary much more in this lesson...and an application problem would have been nice:/ I am currently slowing down on new lessons to try and Close Caption my current videos.
thank you so much for explaining it step-by-step for us! spent weeks trying to figure out how to solve ARC problems online while overlooking your video... better late than never is all I can say after searching for a good tutorial. The tutors at my college are not that helpful.
Me too Nora Abdel ...I hope you pass it like BAM!!! Thanks for watching, learning and subbing and after you pass that midterm I hope you'll have time to tell all your friends, classmates and teachers where to find my channel so they can watch, learn, subscribe and share it too...this helps free educational channels like mine remain free to help everyone :D
WOW...that's the kind of motivation teachers want to hear about! That's awesome:) see me smiling. Those are the kind of study habits that will make college life much easier to get through:) Keep my channel on your likes list when school starts and be sure to tell your friends about it too:D Thanks for choosing Tarrou's Chalk Talk to learn from.
Funny...I've tried to mimic his talent many times, with no luck:( Unless it comes with an instructional video, the talent will remain his! Thanks for thinking of me and learning from my channel:)
You are so welcome Wendell Pfeffer ! Thanks for choosing #ProfRobBob to learn from and don't forget to subscribe and share my channel with everyone...BAM!!!
Hello Mr.Tarrou, if I have the interval of [8,11] and a function of f(x)=(19)/(x-17); is the following solution correct?: if f(x)=(19)/(x-17); then f(8)=(19)/(8-17)=(19)/(-9)=(-19)/(9) and if f(x)=(19)/(x-17); then f(11)=(19)/(11-17)=(19)/(-6)=(-19)/(6) so average rate of change = ((-19)/(6))-((-19)/(9)) = ((-19)/(6))+((19)/(9)) = =((-57)/(18))+((38)/(18)) = ((38)/(18))-((57)/(18)) = (38-57)/18 = (-19)/18 average rate of change = -19/18
How did you figure out which coordinate is x1y1 and x2y2 ? Does it matter if it's the other way around?, beacuse the values change. Btw, great video, Thanks.
That was good. The drawing of the MPG graph bothered me as I think the end behavior of the line would terminate at some point above zero but you drew an arrow.
What if I'm given a word problem such as: "Suppose 2 sec after starting, a dragster is traveling 40mph, and 5 sec after starting, the dragster is traveling 130mph. What is the average rate of change of the speed of the dragster over the time interval from 2 sec to 5 sec?
ok, I have a question. In your first example you used 2 from the (2,-2) ordered pair when you plugged in f(x2)value. But on the second example you plugged in 30 for f(x2), but isn't 30 the y value in the ordered pair and not the x value?
Function notation f(x) is basically a fancy way of writing y. It represents the y value from the function, but also includes the function name 'f' and what x gave that y value. With the point (35,30) the x is 35 and f(35) = 30... y=30
right, but in your second example it appears as if you used the y value where the x value should have been used. You used 30 when you should have used 35 right?
Oh ok, it confused me because in the first example you wrote it as (x1,y1) and (x2,y2) and in the second example it was written as (x1,x2) and (y1,y2). You changed the notation that it was written in between examples. Or am i missing something? Also, does the mpg numbers refer to the y values? I am still confused because if you look at the second example, you plugged in numerator x2 as 30, then you plugged in denominator x2 as 35. How did x2 change from 30 to 35 in your example? If the second example is referring to 30 and 8 being y values,(f(x), then what is going on in the first example. In the first one, you used the actual x values as the plugin for numerator f(x2) and f(x1). It appears as if first example completely contradicts second example and vise versa. But then again, maybe I am missing something. If you can explain that to me that would be greatly appreciated.
Oh, disregard! You explained my questions at 4:35 i missed it, i had to take a bathroom break and i missed that part. Boy do I feel sheepish. Sorry Math sensei. Your superior tutelage puts me to shame.
THANK YOU for the sub and support...please share with everyone and remind them to do the same and keep spreading the word to help us keep growing and helping others:D
This concept can be seen in College Algebra as a framework for practicing/working with function notation, same in early PreCalculus, and in Calculus at the beginning of developing the definition of a derivative.
Hey ProfRobBob I'm a little confused on the second example (the MPG one); why does the top half of the equation become the Y values of the coordinates on the graph? PS: Been binge watching all of your videos, you're awesome!! Your students are lucky lol.
nuwn He starts explaining that at 1:50, in basic algebra we learn rise/run can also be found as y2-y1/x2-x1. but the technical term for the top half y values is f(x2) and that's a fancy way of saying y1 value because the answer to a function is the Y value, and so the answer to the function f(x1) is the y1 value. Just another fancy way of saying y2-y1!
+Tb217741 Do you mean in the denominator? 2- ( - 1), subtracting a negative number is the same as addition so you have 2+1 is 3. Remember that a negative number times a negative number gives a positive product... or answer. So 2- ( - 1) is like 2 - 1 ( - 1) and multiplying the two negative ones gives positive one.
I presume, that the joke of the shirt, lies in the following absurd statement: "5/4 of people, do not understand fractions" 5/4 of people cannot be defined in very meaningful way in this sentence. Sentence claims, that 125% of people do not understand fractions. Yet the number of people at any given time, is 100% of the people, at that time. So, the sentence makes a claim in the future. This statement also claims, that in future, the number of the people, will increase by 25%, when compared to the number of people currently. It cannot be ascertained, whether the number of people will actually grow by 25% in the future... Maybe the statement is a bolder claim, the assumptions of which are: that nobody understands fractions at the moment, and also that nobody will ever understand fractions in the future. Assuming such a case, then, the effect of a 25% increase, would cause the statement to be true.
I'm finally going to college 9 years after high school and you're really helping me get calculus ready. Thank you!
CONGRATS Morgan...that's a big step to take!
You're welcome and thanks for taking the time to like, sub and thank the teacher already:)
Please take every opportunity to share this free resource with everyone, especially classmates and teachers so we can remain free and continue to grow and help others...BAM!!!
you are helping me soo much through calculus in college right now... God Bless You!!!!!!
Thanks for studying with Tarrou's Chalk Talk...please return the help by taking the time to like, sub and share this free educational channel with everyone:D
im doing this in the 8th grade
You are so welcome...thanks for choosing my videos to watch and learn from!
Ok I know Im suppose to be focused on math, BUT...every video that ProfRobBob does I always find myself saying, "Wow...I love his handwriting!" GREAT videos! Thank you!!!!
Stupid. I write like that too
Video 19 in my slowly growing Calculus playlist. Look for Instantaneous Velocity and Speed of Linear Motion. It is a full lesson where I compare average velocity to instantaneous velocity and discuss the difference between velocity and speed.
You're a great teacher! And you helped me pass this week's homework! I don't leave comments, but I had to this time to show how appreciative I am. I especially REALLY liked that you explained the slope in the second problem. It really helped to understand the problem even more. Thank you.
Don't stop making videos! I know I am going to need it for next week too. lol.
Have a good weekend. BAM!
Thanks for choosing #ProfRobBob to watch and learn from GOREjess7 and taking the time to comment and thank the teacher! I hope you will take the time to help us groW by liking, subbing, supporting the ads and telling others to watch and do the same:D After you sub, you'll be able to find me all the time whenever you need that extra little bit of help the next time...BAM!!!
:D...that's me laughing out loud at your reply! You sound just like one of my favorite classroom students...lol
Makes me proud to be your "teacher" too!!! Just for that, I'm going to work even harder at trying to master the dash and will feature it on a video...and when I do, I will dedicate that video to you Hayden...(and will let you know where to find it:)
your teaching method is really student friendly and i like that you explain the meaning of the things, many teachers overstep those explanations.
Thanks for tuning in...glad to hear you like my channel!
Please take the time to sub and share this free resource with everyone...BAM!!!
(especially your teacher:)
@@profrobbob i teach myself. i started to learn math on my own because i find it beautiful :)
@@MrMarkgyuro That's awesome, I hope you continue that passion for math and thanks for choosing my channel to learn from:)
@@profrobbob with these kinda videos, guys like me are just getting more hungry for new things to learn :)
@@MrMarkgyuro that's something every teacher loves to hear:)
In calculus, the concept of derivitives, you will learn how to find the slope of a curve line at a given point...or value of X. Hence, you will find that slope varies with x along a curve. Outside of derivitives, slope is a constant rate of change defined as "change in y per one unit of change in x." So to answer your question here...no...slope is not ax+b.
Thank you for watching and for the kind words:)
#PreCalculus
Thank you so much! I'm in college algebra right now, and my professor is awful. You explained in 10 minutes what he couldn't do in a week!!
Thanks for choosing to watch my lesson. I hope you do great in your class. I have an organized list of lessons here for more help. And please help by spreading the word about my free math lessons:) www.profrobbob.com/algebra-2 or www.profrobbob.com/pre-calculus
And THANK YOU for seeking additional help and choosing my channel to learn from. I'm totally humbled to even have Kahn used as a comparison from you:) I hope you will keep me in mind if you ever need more help or just as an alternate learning channel! Please share your discovery with your friends too...my wife and I are working very hard to groW my channel and spread the word:D
Professor RobBob ,thank you for a solid analysis on the Average Rate of Change and also the true definition of a Slope. Average rate of change is also covered in Calculus One.
no, YOU're awesome for sharing!...THANK YOU so much for supporting our efforts to groW my channel:D We really appreciate your help.
I'm happy to hear that you are enjoying your learning experience from Tarrou's Chalk Talk so much!
THANK YOU! I love teaching and sharing my passion with students who are willing to take that extra step and get outside help...thanks for being one:) Don't forget to spread the word:D
Thank you so very much for all the support! I really appreciate all the "likes" on your channel page and thank you too for subscribing:) Please spread the word to your friends too:D
I couldn't math without you
So helpful and what I really like is he explain things very clear and much better than my professor.
Thanks for watching, learning and subbing Dilnaz Afghan ! Glad it helped:)
Please share my channel with the rest of your class and please remind them to like and sub and support the ads to help us keep growing:D
Hi Mr. Tarrou, it was just today, while reviewing some PreCalculus that I realized I needed to clarify "average rate of change". Of course, it is not a difficult concept (if you already understand slope of a line), but this is still a useful lesson. I just made a small donation to acknowledge the contrbution you have made to my education.
You're welcome...thank you for seeking extra help and choosing my channel:)
I was so stuck on a problem similar to this and my textbook did not help me much, thanks for the video!!
Glad it helped...please help us by sharing this free channel with everyone:D
Thank you for taking the time to do these great videos. I thoroughly enjoy them sir.
Even in summer you have to make sure you know what you're doing for next year x) I'm starting advanced pre-cal as a junior and your videos are a big help. Thank you so much for posting them and keep doing what you do:)
-Emily in Texas
college algebra/precalc are kicking my ass. but these videos make my days a little bit easier so thank you so much!
I prefer to have the point with the largest x value be point 2 but it will work either way.
For once in my life I feel like I can actually understand math again. I'm currently taking Pre-Calculus/Algebra 3 with trigonometry and this is my final year of high school, and I'm very happy to say that I'm definitely gonna subscribe to your channel so I can be able to pass this class AND be able to understand what I've learn when I'm out of high school. I'm glad your channel exists Prof. Rob Bob :D
+Fairy T. and I'm happy to hear that you have found this channel so helpful!
Thanks for investing in your education and taking the time to study and find outside help and for choosing my channel to learn from and support:)
We also thank you for taking the time to share your appreciation and wish you all the best in the future.
Wow, really clear examples, I understand now. Thanks
Perfect! Exactly what I needed to see.
BAM!!!...please sub and share this free channel with everyone!
you are such a great teacher! I prefer hearing you over my think cuban-accented teacher LOL
thanks again for taking time to teach alot of confused kids!
Thank u so much! I subscribed because u do such helpful explanation in this video and in every video you do. And I'm 100% you explain better than my 8th grade teacher. I just wish I was in your class than in her class right now.
Thanks for seeking outside help and choosing this channel to study from...sounds like a good time to share my channel with your teacher so all the rest of the students who want to study at home will know where to find this free study help and you could also get a group of classmates and watch the videos and work on homework together...it's the next best thing to being there...BAM!!!
Thanks for your great teaching skills!
Thank you for all your studying A Lauris !
Thanks for watching!
Thank you so much! This was very clear, helped a lot with my distance methods work!
You're welcome...thanks for liking and choosing Tarrou's Chalk Talk to learn from! Please share with others and remember to support and SUBSCRIBE:)
11:16 What if you had to determine the average rate of change, between 70mph and 20mph. In other words car is decelerating from 70mph to 20mph.
Obviously speed of a car, cannot be negative, because speed of a car, is not a vector quantity ; speed only has magnitude. But at the same time, All cars can decelerate or accelerate, or travel at constant speed. This is proven fact, indeed!
Would you calculate the problem in the same way, in case of a decelerating car?
Getting myself all prepared for college with this videos >:)
What graph is upside down?
Thank you for this video! I have been using Khann Academy, but the videos for average rate of change are awful. This was explained clearly and in an understandable way. Thanks!
I have been studying it, and it looks like the distance between the dashes is proportional to the speed of his arm. Which leads me to think it is how he is holding the chalk that makes it work. I don't have a chalk board to test my theory on, but I think he may be holding it loosely between his fingers with it aimed against the direction of travel so it jumps as he goes. hahaha I just really think you can do this Mr Tarrou! Thank you for replying, hope your doing well! Hayden
Look at you watching more videos, now that's AWESOME hearing the words love and math in the same sentence!...I just sent you a long reply to your flattering last comment:) Please share your experiences with your friends and classmates and someday maybe we will have that "M" next to my subscriber count!!!!
You know this graph actually helps me understand now what domain and range really is. in this mpg sample the domain or x is the speed, and it's being compared to mpg which is the range. technically speaking the speed could be infinity just like the domain in sin cos tan but the mpg is only limited between a max n min y value, you can only get so many mpg that can't be infinity so that's why it's the y axis or the range. bam! did i get that right? thanks again for all your help!
Hey Prof. Rob Bob, I just subscribed! I am taking pre calculus in college and just watched the average rate of change video. My suggestion would be to go on with the secant line. I looked to see if there was another video for secant line, and there wasn't, at least I couldn't find one.
By the way, you're an awesome teacher!
Kim Heisel The slope of the secant line is the average rate of change and the slope of a tangent line is the instantaneous rate of change, but you will not see that until Calculus. I compare and discuss this in a couple of my Calc videos. I should have used the Secant vocabulary much more in this lesson...and an application problem would have been nice:/ I am currently slowing down on new lessons to try and Close Caption my current videos.
Thank you for your very nice feedback Kim Heisel
Extremely helpful video! Thank you!
You're welcome…and THANK YOU for choosing Tarrou's Chalk Talk and supporting by subscribing!
thank you so much for explaining it step-by-step for us! spent weeks trying to figure out how to solve ARC problems online while overlooking your video... better late than never is all I can say after searching for a good tutorial. The tutors at my college are not that helpful.
first thanks for the nice video, i like the way you move your hand over the graph.
really great video you explain things clearly. hope i pass my pre calc midterm :D
Me too Nora Abdel ...I hope you pass it like BAM!!!
Thanks for watching, learning and subbing and after you pass that midterm I hope you'll have time to tell all your friends, classmates and teachers where to find my channel so they can watch, learn, subscribe and share it too...this helps free educational channels like mine remain free to help everyone :D
You are a great teacher !!!
THANKS ivan delgado !!!
Video was very useful for me. Thank You!
You're welcome Nathaniel...thanks for watching...please share this channel with your classmates and teacher:D
Your awesome! If anyone needs help in math, I am sure to tell them about you!
WOW...that's the kind of motivation teachers want to hear about! That's awesome:) see me smiling.
Those are the kind of study habits that will make college life much easier to get through:) Keep my channel on your likes list when school starts and be sure to tell your friends about it too:D Thanks for choosing Tarrou's Chalk Talk to learn from.
Hey Mr. Tarrou! You should do dashed lines like this! Look up: His Hand Doesn't Even Move on RUclips. You're videos never cease in helping me. :)
Thank you for all your videos! Just wondering, how did you get that graph paper grid on the board? Did you draw it all?
+Revera Mirrors you're welcome, thanks for watching!
I have a pull down grid that was made to use with a chalkboard:)
Thank you for the nice words:)
Funny...I've tried to mimic his talent many times, with no luck:( Unless it comes with an instructional video, the talent will remain his! Thanks for thinking of me and learning from my channel:)
your really awesome! can u make a video of instantaneous rate of change (IROC) please i will be very thankful to you
Wow I understand this perfectly now thank you so much!!!!
You are so welcome Wendell Pfeffer !
Thanks for choosing #ProfRobBob to learn from and don't forget to subscribe and share my channel with everyone...BAM!!!
thank you so much you explained this so clearly
You're welcome dragonhunter1120 thanks for choosing #ProfRobBob to learn from and subscribe to:)
enjoying the videos very much. thank you very much.
Hello Mr.Tarrou, if I have the interval of [8,11] and a function of f(x)=(19)/(x-17); is the following solution correct?:
if f(x)=(19)/(x-17); then f(8)=(19)/(8-17)=(19)/(-9)=(-19)/(9)
and
if f(x)=(19)/(x-17); then f(11)=(19)/(11-17)=(19)/(-6)=(-19)/(6)
so
average rate of change = ((-19)/(6))-((-19)/(9)) = ((-19)/(6))+((19)/(9)) = =((-57)/(18))+((38)/(18)) = ((38)/(18))-((57)/(18)) = (38-57)/18 = (-19)/18
average rate of change = -19/18
Have you heard of Wolfram Alpha? It's very helpful.
Yes I have. Thank you for the suggestion.
You just saved my ass in my pre-calc class. Thank you so much!
How did you figure out which coordinate is x1y1 and x2y2 ? Does it matter if it's the other way around?, beacuse the values change.
Btw, great video, Thanks.
That was good. The drawing of the MPG graph bothered me as I think the end behavior of the line would terminate at some point above zero but you drew an arrow.
You're right Keith Tucker I should have had it taper down to the right, approaching a horizontal line of y=0
Thank you so much! This was very helpful :)
What if I'm given a word problem such as: "Suppose 2 sec after starting, a dragster is traveling 40mph, and 5 sec after starting, the dragster is traveling 130mph. What is the average rate of change of the speed of the dragster over the time interval from 2 sec to 5 sec?
make it an x and y problem. Draw a graph and mark the seconds as x and the MPH as y. From there you just solve.
thanks for helping Josh!
Thank you so much for your awesome videos
@MultiRedman7 Every Friday is funny t-shirt day. Thanks
ok, I have a question. In your first example you used 2 from the (2,-2) ordered pair when you plugged in f(x2)value. But on the second example you plugged in 30 for f(x2), but isn't 30 the y value in the ordered pair and not the x value?
Function notation f(x) is basically a fancy way of writing y. It represents the y value from the function, but also includes the function name 'f' and what x gave that y value. With the point (35,30) the x is 35 and f(35) = 30... y=30
right, but in your second example it appears as if you used the y value where the x value should have been used. You used 30 when you should have used 35 right?
All the numbers are where they belong. (Y2-Y1)/(X2-X1) or in function notation(f(X2)-f(X1))/(X2-X1)
Oh ok, it confused me because in the first example you wrote it as (x1,y1) and (x2,y2) and in the second example it was written as (x1,x2) and (y1,y2). You changed the notation that it was written in between examples. Or am i missing something? Also, does the mpg numbers refer to the y values? I am still confused because if you look at the second example, you plugged in numerator x2 as 30, then you plugged in denominator x2 as 35. How did x2 change from 30 to 35 in your example? If the second example is referring to 30 and 8 being y values,(f(x), then what is going on in the first example. In the first one, you used the actual x values as the plugin for numerator f(x2) and f(x1). It appears as if first example completely contradicts second example and vise versa. But then again, maybe I am missing something. If you can explain that to me that would be greatly appreciated.
Oh, disregard! You explained my questions at 4:35 i missed it, i had to take a bathroom break and i missed that part. Boy do I feel sheepish. Sorry Math sensei. Your superior tutelage puts me to shame.
if the slope is m in f(x)=mx+b, then wouldn't the slope be ax+b in f(x)=ax*x+bx+c? {which equals (ax+b)x+c}
You are the BEST!!
THANK YOU for the sub and support...please share with everyone and remind them to do the same and keep spreading the word to help us keep growing and helping others:D
BAM! I like your approach. Thanks.
Is this for College Algebra or Pre-Calc? It doesn't say in the description box.
This concept can be seen in College Algebra as a framework for practicing/working with function notation, same in early PreCalculus, and in Calculus at the beginning of developing the definition of a derivative.
Thanks for the video Prof !
You're welcome Moran Elhija don't forget to like, SUBSCRIBE and share my channel with others:D
Thank you
:)
@angie4779 Thank You:):):)
Hey ProfRobBob I'm a little confused on the second example (the MPG one); why does the top half of the equation become the Y values of the coordinates on the graph?
PS: Been binge watching all of your videos, you're awesome!! Your students are lucky lol.
nuwn He starts explaining that at 1:50, in basic algebra we learn rise/run can also be found as y2-y1/x2-x1. but the technical term for the top half y values is f(x2) and that's a fancy way of saying y1 value because the answer to a function is the Y value, and so the answer to the function f(x1) is the y1 value. Just another fancy way of saying y2-y1!
HERKFOOT21 Thank you so much for the help:D:D:D
THANK YOU, THANK YOU, THANK YOU !!
+deltaexplorer47 YOU'RE WELCOME!!!
+Swift Junk :)
OK! hahaha Sounds awesome! Thanks Mr. Tarrou, can wait to see it! :D
You're welcome:)
Great video, Thanks.
@amadeusemozart Thank you:):):)
very clear..thank you!!
U R awesome teacher !!! THX a lot : )
Where did you get the 3??
+Tb217741 Do you mean in the denominator? 2- ( - 1), subtracting a negative number is the same as addition so you have 2+1 is 3. Remember that a negative number times a negative number gives a positive product... or answer. So 2- ( - 1) is like 2 - 1 ( - 1) and multiplying the two negative ones gives positive one.
+ProfRobBob Not that one. I'm talking about the 3 in the formula
+Tb217741 y=x^2-3x??? That is the function I just made up for the example. The -3 in the numerator that shows up twice is from the given function.
No BAM? :(
This man looks like a demolitions expert
Never heard that comparison before...Must have something to do with my 25 years of teaching high school :( Thanks for watching and learning!
I am not sure what order to watch these to skip the stuff I know and get to the stuff I don't xD
Thank you, sir.
+LilKidAttacker you're welcome...please take the time to like, sub and share this free educational channel with others:D
This helped so freakin much
Not sarcastic at all man
BAM!!!
...none taken:)
I want that shirt!
+Eric Olalde there are versions everywhere...but you'd be surprised how many people DON'T get it...lol
I keep reading your t-shirt ! Can't concentrate at all!
Math humor...sorry for the distraction!
Please sub and share the lessons and attempt at humor...BAM!!!
his pants are up to his belly button
God bless your soul
Thank you:)
Thanks !
I presume, that the joke of the shirt, lies in the following absurd statement: "5/4 of people, do not understand fractions" 5/4 of people cannot be defined in very meaningful way in this sentence.
Sentence claims, that 125% of people do not understand fractions. Yet the number of people at any given time, is 100% of the people, at that time.
So, the sentence makes a claim in the future. This statement also claims, that in future, the number of the people, will increase by 25%, when compared to the number of people currently. It cannot be ascertained, whether the number of people will actually grow by 25% in the future...
Maybe the statement is a bolder claim, the assumptions of which are: that nobody understands fractions at the moment, and also that nobody will ever understand fractions in the future. Assuming such a case, then, the effect of a 25% increase, would cause the statement to be true.
Haha, you summed up my shirt in the first paragraph! A surprising number of people do not understand that t-shirt:)
great!
cool shirt
Thanks walter white ...it's surprising how many people "don't" get it :)
love he shirt sir, 5 out of 4 hahahahaha
Thanks!
...funny, you'd be surprised how many people DON"T get it:(
Good to see you watching so many videos too, I hope your sharing them...BAM!!!
the graph is upside down