1. Special Functions and Graphs Algebra II …………… Sections 2.7 and 2.8

2. SWBAT  identify, graph and write absolute value functions  graph a function based on translations and transformations  graph and find the value of a piecewise defined function  graph the greatest integer function

3. Vocabulary  absolute value function  vertex  transformation  translation  parent function  reflection  piecewise function  step function

4. Absolute Value Function  symmetric about y-axis  for every (x, y) there is a point (-x, y)  vertex - point where sides come together  parent function - basic function, vertex is (0, 0)

5. General Equation  vertex: (h, k)  horizontal shift: x - h = 0  vertical shift: k  shape of graph remains the same

6. Examples  For each equation, state the vertex, describe the translation and sketch the graph

7. Transformations  s hape of the graph changes  stretch = more narrow  shrink = wider  vertical stretch: vertical shrink: reflection (about x-axis):

8.  vertical ___________ by factor of ______  vertex is ___________  find point on each side of vertex

10.  reflected about _____________  vertical _________ by factor of _______  vertex is __________  two more points

12.  vertex is ________  reflected about _________  vertical __________ by factor of _______  two more points

14. Write the equation of the graph

15. Sketch additional graphs  Use the graph to sketch  (a)  (b)

16. Piecewise Function  defined by different expressions, each with a separate domain  ex]  Find f(-3) and f(1)

17.  Graph the function:

19.  Write a piecewise function from the graph

20.  Write the piecewise function from the graph

21. Greatest Integer Function (step function)  greatest integer not larger than the given value