Graphing Techniques Q&A (1 of 3: Horizontal transformation example)

[TheBigMeme]

I could never tell if you were Australian or English, but the rugby analogy solved the problem for me.

[沈博智-xy]

another way to think about f(ax - b)

first translate b units to the right
then with the current translated graph you have, (x, y) values turn into (x/a, y)

In the context of this example:

f(x) has points at (-1, -5), (0, 0), (1, 3), (2, 4), (3, 3), (4, 0), and (5, -5)

we want f(2x-6)

first, translating six units to the right gives

(-1 + 6, -5), (0 + 6, 0), (1+6, 3), (2+6, 4), (3+6, 3), (4+6, 0), and (5+6, -5)
(5, -5), (6, 0), (7, 3), (8, 4), (9, 3), (10, 0), (11, -5)

Then applying the dilation:
(5/2, -5), (6/2, 0), (7/2, 3), (8/2, 4), (9/2, 3), (10/2, 0), (11/2, -5)

We get our points (2.5, -5), (3, 0), (3.5, 3), (4, 4), (4.5, 3), (5, 0), (5.5, -5)

[wispybell]

Translating to the right 6 and compressing the function horizontally by half will result in the same graph. The common mistake there is compressing with respect to the vertex rather than the y-axis.

[henryzheng]

I am confused somehow... Are we really applying the order operation to the transformations? Because it seems to me that with f(2(x-3)), the order of operations says to take care of whatever is inside the parenthesis first, but we're actually doing the horizontal shrink which is the multiplication that is outside the parenthesis. I feel like we are more like following the order of "unwrapping an expression/equation". Shifting 6 units right then shrinking half is the same as shrinking half then shifting 3 units right. Now I just don't see the point of factoring what's inside the f( ) if we just want to graph a function.

[yaxjoshi]

lol i enjoy watching Eddie teach rather then the videos my teacher makes

[syedziaulhaque]

Your explanation is pretty good as usual however, I have a point to clarify. As for the order of transformation, shouldn’t it be opposite of bidmas as they are connected with only horizontal transformations?

[yanengganak]

Bro i understand now. Eddie ur the best, thanks 🔥🔥🔥🔥🔥🔥🔥🔥🔥

[TheBallzin]

My professor uses software like statcrunch to teach our class, and then most people like barely follow along but, I see the use of software if you were doing statistics for an occupation like 24/7, but I rather learn by a calculator first, so thanks.

[TheBallzin]

REMEMBER graph initially starts at y= -(x-2)^2 +4 while final position is translated to f2(x-3)

[blakehowell]

I need help with the integral of 2x from 10 to 13

[andrewjolly]

Hi Eddie, what software are you using here? I use desmos when I teach this sort of thing but I'd love to be able to write on the screen like that without having to switch back to openboard.

[marshallchiasson]

I think I'm really rusty because if you plug in an x value of 4 in the final equation shouldn't you get a y value of 5?

[jossenaert]

How old are the students that this lesson is for?