1. Piecewise Functions Pieces of 2 or more relations Final graph is a function (passes vert. line test) CALCULATOR: – Y= (function)(restriction) – Restriction: x 2 nd MATH choose inequality

2. Greatest Integer Function [[x]] “Rounding down” or “Step” function Each step 1 unit long Each step up 1 unit from last Each step closed on left & open on right. Initial step of parent starts at (0,0) – Add - up or Subtract - down – Add inside - left or Subtract inside - right – Multiply - steepness

3. Greatest integer function with calculator Math → NUM 5:int( Enter values inside [[x]] inside ( ). MODE – DOT (not connected)

4. Examples 1.) Graph the piecewise function by hand & with the calculator. F(x) = x² -1 x> 1 2x + 3 x < 1 Calculator: y₁ = (x² - 1) (x 2 nd MATH > 1) y₂ = (2x + 3) (x 2 nd MATH < 1) MODE – DOT - GRAPH

5. More examples Graph by hand and with the calculator. – A) [[x]] + 4 – B) [[x -3]]