Quick Crisp Review Graphing a piecewise function Determine relative max and min Graphing a step function 35)a) oddb) even (-3/2, 4)

Answers to Homework For all graphs see back of book Increasing (-2, ∞) decreasing (-3,-2) neither odd nor even 31)Odd 35)a) (1.5,4) b) (1.5,-4) 39)Neither 47)See Back of Book 51)(3,-9) 53)Relative Min (1, -7) Relative Max (-2,20) 59) Domain (- ∞, ∞) Range [0,2) 63) (- ∞,4]67) [-1,1]

You will be able to transform graphs given the equation. Date Many graphs are transformations of common functions. Rigid transformation changes location not size. Vertical Shift: f(x) = x 2 + c (up) f(x) = x 2 – c (down) Lets start with f(x) = x 2

Horizontal Shift: f(x) = (x – c) 2 (right) f(x) = (x + c) 2 (left) Reflection f(x) = -x 2 (over x-axis) f(x) = (-x) 2 over (y-axis) Stretch: Multiply y- coordinates f(x) = cx 2 (stetched vertically) f(x) = x 2 /c (stretched horizontally

Sequence of Transformations A function involving more than one transformation can be graphed by performing transformations in the following order. 1. Horizontal shifting 2. Vertical stretching or shrinking 3. Reflecting 4. Vertical shifting

Class Assignment Draw a graph that represents f(x). Give an example of a vertical shift, horizontal shift, reflection, and a stretch. Example f(x) Vertical Shift: f(x) + 2 (shift everything up 2)