1.7 Absolute Value, Greatest Integer, & Piecewise Functions - PowerPoint PPT Presentation

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1.7 Absolute Value, Greatest Integer, & Piecewise Functions

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  1. 1.7 Absolute Value, Greatest Integer, & Piecewise Functions

  2. Greatest Integer Function: greatest integer ≤ x numerical ex: Ex 1) Graph for –3 ≤ x ≤ 3 It’s a function! (passes vertical line test) *graphing calculator MATH  NUM  int( y x

  3. Ex 2) Graph for –3 ≤ x ≤ 3 y x

  4. *graphing calculator MATH  NUM  abs( Absolute Value Function: numerical ex: Ex 3) Graph y x

  5. Ex 3) Graph *Hint: Remember number addition or subtraction “inside” parentheses or abs values, etc moves function left or right (opposite of what the symbol is) AND addition or subtraction “outside” move up or down y x

  6. Interval notation: • If you use infinity, always use open notation: • How does a graph behave on an interval? • Increasing – goes up as you go to right • Decreasing – goes down as you go to right • Constant – stays level/ horizontal as you go to right open: (a, b) closed: [a, b] a a a a b b b b [a, b) half-open: (a, b]

  7. Piecewise Function: function is defined differently over various parts of the domain Ex 5) Graph the piecewise function. State the open intervals f(x) is increasing, decreasing, or constant. Is the function continuous? y x Inc: (0, 1) Const: Yes!

  8. Homework #107 Pg 47 #3, 4, 6 – 8, 10 – 19 all, 21 – 43 odd