Function Transformations: Horizontal and Vertical Stretches and Compressions

This video explains to graph graph horizontal and vertical stretches and compressions in the form a*f(b(x-c))+d. This video looks at how a and b affect the graph of f(x).

[countzero]

13 years later and it's still helping people.
Thanks alot sir.

[ivanherrera]

Really appreciate. This is by far, the most helpful math tutor I've find in all youtube. Saved my gpa, saved my marriage, saved my life....thanks so much!

[gabooshi]

11 years later and this video still saving us ...

[kickingcat]

Thank you so much. I was learning vertical stretches and compressions from a book, and they were not clicking at all. Now I realize how simple they are!

[-lnmv.]

Really helpful, I searched for this point for a quadratic and cubic function but never found one, until this poped up. What a legend

[TelepathShield]

So basically vertical stretch and compression is changing the y values by a number. 3f(x) is multiplying (or stretching) the y values by 3, whereas 1/3f(x) is dividing by 3 (aka compressing by a factor of 1/3). Horizontal stretch and compression is the same thing but inside the function. Also for horizontal stretch and compression, the values are reciprocal-ed, so f(1/3x) is horz. stretch not conpression. F(1/3x) is tripling the x values, and f(3x) is dividing the x values by 3. I hope this makes sense because it took me a while to try and figure this out.

[lilsmarty]

ok guys so if you still dont get it...

for vertical stretches and compressions
a>1 means that a is not a fraction or decimal
and
0<a<1 means that a is a decimal or fraction which means it is a is a number between 0 & 1

hope that helped

[reefym]

Still don’t get it . My test is gonna be less than 12% for a fact

[lexinaut]

Very nice!  You have compressed the information nicely without stretching the truth within it!

[motivatedmind]

helpful!! I am reviewing precalc this summer on my own b/c I have to take Calc 1 this fall. I just read the transformation section today and for some reason it wasn't clicking with the horizontal and vertical stretching part, but your video made it click for me! lol thanks!

[akijohn]

for 'a' and 'k', they are meant to stretch and compress the graph in the same direction; furthermore, the terms stretch and compressed are connected to the relationships the function has with each axis. Thanks for clearing up things!

[davecolombia]

where does logic behind the rule: 'multiply each x-coordinate by 1/b' derive from?

[NoorMarwahGK]

This video came out when i was born Lol. Thanks anyways It helped a lot.

[IndesirableShadow]

In a nutshell,
a(b(x+c)^2)+d
a is for vertical compression or stretch
if 0 < a < 1 Vertical compression.
a> 1 vertical stretch.
while horizontal is opposite.
b is for horizontal comp or stretch
c is horizontal translation if pos goes left if neg goes right aka flipping + or - for direction
d is vertical translation based on symbol

[severed_toast]

how do I know when to stretch a function vertically and when to compress horizontally?

[lizardking]

Thanks for the help! I was stumped over my hw for the past hour and this really helped clear things up!

[MrZak-rfvq]

What program do you use to show the example in real-time?

[doginsomnia]

Bro I’m boutta have the test in an hour and this is the ONLY thing I’ve ever struggled on in math. I’m cooked man

[stefan-tgec]

How did he take the numbers for x for the function g(x)=x/2 and h(x)=2x

[grapeleiva]

whats the difference between the horizantal stretch and the vertical one? in the animation it looks the same. if its less than one its goes farther and and if its greater than one it gets skinnier