transformations of polynomial functions in the form

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 + 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…

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= x2

Memorize the simple graphs…

(0,0)

(2,8)

(1,1)

y= x3

Memorize the simple graphs…

(0,0)

(2,16)

(1,1)

y= x4

Pg 491,4,5