This video looks at transformations of linear functions. Included are vertical translations, rotations, and reflections over the y-axis. Four examples are included.
Thank you so much! My algebra teacher isn't the greatest at explaining things so she generally sticks to textbook instructions. They really don't make sense to me but the way you explained all of this was perfect, thank you!!!!
7 years later in 2020, I'm watching this video studying for the test out and I only have 2 months to study unlike my friends who have been studying for over 9 months. Thank you because you teach really well and quick so i can zoom through chapters really quickly and learn all the concepts.
Thank you, but how would you know if in a combined transformation linear equation the reflection is over y or x axis? In addition, how would you know if it is horizontal shrink or vertical stretch in an combined transformation?
That's a great question! It really depends on the original function you are transforming. If working with the parent linear function f(x) = x, a reflection over the x- or y-axis will yield the exact same result. If you start with something a little more complicated, say f(x) = 2x + 1, we notice that a vertical stretch maintains the x-intercept and "pulls" all the points away vertically. A horizontal stretch will maintain the y-intercept and "pull" all the points away in the horizontal direction. If you graph the following on Desmos (or your favorite graphing tool), you can see the differences. f(x) = 2x + 1 2 * f(x) ---> vertical stretch by factor of 2 f((1/2)x) ---> horizontal stretch by factor of 2 I hope that helps! 👍☺
They're using function notation...remember, whatever is inside the parenthesis is what we put into the function of that name for x. In your problem, the f(x + 5) means that we substitute x + 5 into the function named f everywhere we see an x. That gives us: g(x) = -(x + 5) - 2 From there we can simplify to get: g(x) = -x - 5 - 2 = -x -7 I hope that helps! Thanks for the question! Keep working and asking questions when you're not sure! 👍
how would you solve an equation that went something like g(x)=(3x+5)+8? I have a test coming up and I really need to know this, thanks! This video helped me with the rest of my homework, thank you!
Tell me more about what the question is asking and I will see if I can help!? One tool that is great for figuring out transformations is Desmos.com. It's easy to put numbers in and take them out to see the effect they have on the graph. 👍
@@MartyBrandl sorry about that, of course. It’s asking how the graph of G (which I already told you) compares with the graph of F (which is [f(x)=3x+5]). I wanted to know, would I need to combine 8 and 5 to make 13? I wasn’t sure because 3x and 5 were in parentheses which usually means you have to combine them first. In equations like this am I supposed to ignore parentheses? (i probably should have elaborated more on the problem before i hit comment lol)
@@hexedhydra2554 Ok, having the +8 outside the parentheses is actually kind of helpful! That's the only difference between the two functions and we can see the change by looking at the y-intercept. f has a y-intercept of 5 and g has a y-intercept of 13. What happened? It's moved up 8 units. I hope that helps! Keep working hard and asking great questions! 👍
If the original function had a y-intercept of 0 that would be true, but a vertical stretch on the f(x) would also change the y-intercept. The rotation idea isn't used a commonly as the vertical stretch though, so I can see where the confusion comes in. I hope that helps!?
The + 4 without the parenthesis will move the graph up 4 units. The parenthesis added will move it graph 4 units to the left. Desmos is a great graphing tool that you can use to type in an equation in function notation and then type in the transformations to see how the graph changes! I hope that helps! Keep asking great questions! 👍
![ЛЕБЕДЕВ у ДУДЯ: муху не обманешь 😁 [Пародия]](http://i.ytimg.com/vi/E74h5fvVrqs/mqdefault.jpg)
Thank you so much! My algebra teacher isn't the greatest at explaining things so she generally sticks to textbook instructions. They really don't make sense to me but the way you explained all of this was perfect, thank you!!!!
Ashley Fox same here
7 years ago and this man still helps people, I finally understand linear functions!
7 years later in 2020, I'm watching this video studying for the test out and I only have 2 months to study unlike my friends who have been studying for over 9 months. Thank you because you teach really well and quick so i can zoom through chapters really quickly and learn all the concepts.
Oh my goodness this actually saved me
Thank you! This was a very helpful explanation.
Thanks! This helped me with my homework!
THIS IS AMAZING thank you so much!
Thank you! Very helpful
math videos are really timeless
thanks bro helped me pass the 111th grade
Thank you so much!!
thx a lot , these videos help me a lot
Thank you!
this was very hepful thanks
Thank you! :)
very VERY helpful for my homework....otherwise i was boutta be lost
Dang, thanks bro 👊🏿
Thank you now I understand the math
Very helpful
Very helpful for my exam tomorrow thanks a lot !
kaa-chaan !!😂😂
Thank you! This helped me SOO much!!
thank yooooou this topic has me failing 8th grade rn it really helped
Thank you, but how would you know if in a combined transformation linear equation the reflection is over y or x axis? In addition, how would you know if it is horizontal shrink or vertical stretch in an combined transformation?
That's a great question! It really depends on the original function you are transforming. If working with the parent linear function f(x) = x, a reflection over the x- or y-axis will yield the exact same result.
If you start with something a little more complicated, say f(x) = 2x + 1, we notice that a vertical stretch maintains the x-intercept and "pulls" all the points away vertically. A horizontal stretch will maintain the y-intercept and "pull" all the points away in the horizontal direction.
If you graph the following on Desmos (or your favorite graphing tool), you can see the differences.
f(x) = 2x + 1
2 * f(x) ---> vertical stretch by factor of 2
f((1/2)x) ---> horizontal stretch by factor of 2
I hope that helps! 👍☺
In our answers, when are we supposed to use the slope and steepness and when are we supposed to use y intercept?
Mo Kai It depends on what the problem is asking for. Read carefully! :-)
Omg I actually understand thank god bc my exam is in an hour
so much better than khan academy
Thank UUUUU
Could possibly explain the equation f(x)=-x-2; g(x)=f(x+5) I don't know what I'm supposed to do with the 5 in the parenthesis at the end?
They're using function notation...remember, whatever is inside the parenthesis is what we put into the function of that name for x.
In your problem, the f(x + 5) means that we substitute x + 5 into the function named f everywhere we see an x. That gives us:
g(x) = -(x + 5) - 2
From there we can simplify to get:
g(x) = -x - 5 - 2 = -x -7
I hope that helps! Thanks for the question! Keep working and asking questions when you're not sure! 👍
how would you solve an equation that went something like g(x)=(3x+5)+8? I have a test coming up and I really need to know this, thanks! This video helped me with the rest of my homework, thank you!
Tell me more about what the question is asking and I will see if I can help!?
One tool that is great for figuring out transformations is Desmos.com. It's easy to put numbers in and take them out to see the effect they have on the graph. 👍
@@MartyBrandl sorry about that, of course. It’s asking how the graph of G (which I already told you) compares with the graph of F (which is [f(x)=3x+5]). I wanted to know, would I need to combine 8 and 5 to make 13? I wasn’t sure because 3x and 5 were in parentheses which usually means you have to combine them first. In equations like this am I supposed to ignore parentheses?
(i probably should have elaborated more on the problem before i hit comment lol)
@@hexedhydra2554 Ok, having the +8 outside the parentheses is actually kind of helpful! That's the only difference between the two functions and we can see the change by looking at the y-intercept. f has a y-intercept of 5 and g has a y-intercept of 13. What happened? It's moved up 8 units.
I hope that helps! Keep working hard and asking great questions! 👍
Helpful
Hello, I have a test coming up, I still don't understand wat a transformation of a linear function is
It's basically just a change in the slope or the y-intercept from the parent linear function f(x) = x
@@MartyBrandl Thank you!
Thanks im taking a test rn
Blessss
Thank God, I have finals tmmr
Blake Underwood same its 1 am lol
For the second equation, shouldn't you explain that the graph was say vertically stretched by a factor of 1.5?
If the original function had a y-intercept of 0 that would be true, but a vertical stretch on the f(x) would also change the y-intercept. The rotation idea isn't used a commonly as the vertical stretch though, so I can see where the confusion comes in. I hope that helps!?
So what happen if f(x)= 4x + 4 compared with f(x) = 4(x+4) ??
The + 4 without the parenthesis will move the graph up 4 units. The parenthesis added will move it graph 4 units to the left.
Desmos is a great graphing tool that you can use to type in an equation in function notation and then type in the transformations to see how the graph changes!
I hope that helps! Keep asking great questions! 👍
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