transformations of polynomial functions in the form
DESCRIPTION
1. We need to decide on some key points to track for each power function…. X = {-2, -1, 0, 1, 2} Return to your original Power Function activity, and label the exact points for these given x values… memorize themTRANSCRIPT
![Page 1: Transformations of Polynomial Functions in the form](https://reader035.vdocuments.us/reader035/viewer/2022062306/5a4d1be37f8b9ab0599e0c13/html5/thumbnails/1.jpg)
Transformations of Polynomial Functions in the form
![Page 2: Transformations of Polynomial Functions in the form](https://reader035.vdocuments.us/reader035/viewer/2022062306/5a4d1be37f8b9ab0599e0c13/html5/thumbnails/2.jpg)
In this section, we will investigate the roles of the parameters a,k,d and c in
the polynomial function of the form
y = a[k(x – d)]n + c The values of n will be limited to 2, 3,and 4..
(This is good news….)
![Page 3: Transformations of Polynomial Functions in the form](https://reader035.vdocuments.us/reader035/viewer/2022062306/5a4d1be37f8b9ab0599e0c13/html5/thumbnails/3.jpg)
1. We need to decide on some key points to track for each
power function….X = {-2, -1, 0, 1, 2}
Return to your original Power Function activity, and label the exact points for these given x values… memorize them
![Page 4: Transformations of Polynomial Functions in the form](https://reader035.vdocuments.us/reader035/viewer/2022062306/5a4d1be37f8b9ab0599e0c13/html5/thumbnails/4.jpg)
y = af[k(x – p)]n + qq: Vertical displacement:
+q: up, -q: downp: Horizontal shift:
-p: right, +p: leftk: Horizontal stretch or compress
multiply the “x’s” by 1 / k a: Vertical stretch or compress
multiply the “y’s” by a
“n” determines the degree of the Power Function…
![Page 5: Transformations of Polynomial Functions in the form](https://reader035.vdocuments.us/reader035/viewer/2022062306/5a4d1be37f8b9ab0599e0c13/html5/thumbnails/5.jpg)
We are going to execute the manipulations from left to right
(like reading a book)
Special Note: If there is a horizontal translation, the coefficient for “x” must be factored to “1”.
y = (4x – 8)3 should be written as
y = [4(x – 2)]3
![Page 6: Transformations of Polynomial Functions in the form](https://reader035.vdocuments.us/reader035/viewer/2022062306/5a4d1be37f8b9ab0599e0c13/html5/thumbnails/6.jpg)
Memorize the simple graphs…
(0,0)
(2,4)
(1,1)
y= x2
![Page 7: Transformations of Polynomial Functions in the form](https://reader035.vdocuments.us/reader035/viewer/2022062306/5a4d1be37f8b9ab0599e0c13/html5/thumbnails/7.jpg)
Memorize the simple graphs…
(0,0)
(2,8)
(1,1)
y= x3
![Page 8: Transformations of Polynomial Functions in the form](https://reader035.vdocuments.us/reader035/viewer/2022062306/5a4d1be37f8b9ab0599e0c13/html5/thumbnails/8.jpg)
Memorize the simple graphs…
(0,0)
(2,16)
(1,1)
y= x4
![Page 9: Transformations of Polynomial Functions in the form](https://reader035.vdocuments.us/reader035/viewer/2022062306/5a4d1be37f8b9ab0599e0c13/html5/thumbnails/9.jpg)
![Page 10: Transformations of Polynomial Functions in the form](https://reader035.vdocuments.us/reader035/viewer/2022062306/5a4d1be37f8b9ab0599e0c13/html5/thumbnails/10.jpg)
![Page 11: Transformations of Polynomial Functions in the form](https://reader035.vdocuments.us/reader035/viewer/2022062306/5a4d1be37f8b9ab0599e0c13/html5/thumbnails/11.jpg)