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1.7 Absolute Value, Greatest Integer, & Piecewise Functions

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

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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 2) Graph for –3 ≤ x ≤ 3 It’s a function! (passes vertical line test) *graphing calculator MATH  NUM  int( y x

  3. Ex 3) Graph for –3 ≤ x ≤ 3 y x

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

  5. Ex 5) 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. It is useful to know the intervals in which the graph is increasing, decreasing, or constant. • A function f is an increasingfunction if f (x2) > f (x1) when • x2 > x1 for all x in its domain. • A function f is a decreasingfunction if f (x2) < f (x1) when • x2 > x1 for all x in its domain. • Constant – stays level/ horizontal as you go to right • To write the open intervals in which the graph is inc, dec, or constant, use interval notation: • (left x-value, right x-value) • use – or  if graph goes on forever in that direction (goes up as you go to right) (goes down as you go to right)  NEVER use y-values!

  7. Piecewise Function: function is defined differently over various parts of the domain Ex 6) Graph the piecewise function. State the open intervals f (x) is increasing, decreasing, or constant. Is the function continuous? (the x-values) y x Inc: Dec: (0, 1) Const: No!

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