Post by: oliverk94 on January 19, 2012, 09:31:47 pm
|(x+1)^2-1|-2
Showing all working out?
I've attempted it a couple of times but the answer is different from the back of the book.
Post by: b^3 on January 19, 2012, 11:27:32 pm
i.e.
Start with y=x2
(http://i1082.photobucket.com/albums/j373/mclaren200800/img1.png)
To y=(x+1)2-1 (translation of 1 unit left and 1 unit down)
(http://i1082.photobucket.com/albums/j373/mclaren200800/img2.png)
To y=|(x+1)2-1|. Now the mod will make everything inside that is negative, postivie and everything that is postive to stay positive. That means that anything that is negative (i.e. below the x-axis) will be flipped in the x-axis so that it ends up above it and positive.
(http://i1082.photobucket.com/albums/j373/mclaren200800/img3.png)
Finally transform to y=|(x+1)2-1|-2 (a translation of 2 units down).
(http://i1082.photobucket.com/albums/j373/mclaren200800/img4.png)
After a while you get used to do all of this in your head, although it is useful to sketch the function before the modulus nd then apply the mod (the flipping the stuff below the a-axis above it).
For x-intercepts/t.ps you can either apply the transformations to the points or for the x-intercepts you can do this.
|(x+1)2-1|-2=0
|(x+1)2-1|=2
(x+1)2-1=2 or -[(x+1)2-1]=2
(x+1)2=3 (x+1)2=-1
x=
For the turning point, (0,0)-->(-1,-1)-->(-1,1)-->(-1,1-2)=(-1,-1)
y-intercept, x=0
y=|1-1|-2=-2
(0,-2)
Post by: oliverk94 on January 20, 2012, 10:44:28 am
Are you using the CAS software to sketch?
Post by: pi on January 20, 2012, 10:47:53 am
Post by: Planck's constant on January 20, 2012, 11:26:47 am
Try applying the transformations and then apply the mod and then last transformation.
Even though I use different methods myself, your post is the best I have seen on AN :)
Post by: b^3 on January 20, 2012, 01:53:55 pm
Hey thanks a lot man. Really appreciate it brah.
Are you using the CAS software to sketch?
https://www.abettercalculator.com/calculator/Yeh thats the one I'm using Rohitpi, I like it and it can do a lot of things like output an image, or defining functions and allowing a link that you can give to play around with. I.e I can set something up to explain something and then link to it.
E.g. to explain tangents and slopes and intersecting lines I could give you this link https://www.desmos.com/calculator/c64ccc0dc4 and playing with the o and q sliders :)
Or this https://www.desmos.com/calculator/d9aae69526
And thanks argonaut.
EDIT: Fixed links. If the thing repeatedly trys to reload the page, then clear cookies and try again.