Transformations of Polynomial Functions in the form

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….)

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

y = af[k(x – p)] n + q q: Vertical displacement: +q: up, -q: down p: Horizontal shift: -p: right, +p: left k: 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…

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

Memorize the simple graphs… (0,0) (2,4) (1,1) y= x 2

Memorize the simple graphs… (0,0) (2,8) (1,1) y= x 3

Memorize the simple graphs… (0,0) (2,16) (1,1) y= x 4

Pg 49 1,4,5