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1.7 Difference Quotient, Absolute Value, Greatest Integer, & Piecewise Functions

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1.7 Difference Quotient, Absolute Value, Greatest Integer, & Piecewise Functions

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  1. Cheating Policy:  Cheating is a very serious offense and will not be tolerated.  Students will abide by the Academic Code found in the Student and Parent Handbook.  A student who is in possession of, but not limited to, a cheat sheet, notes, copies of an exam, or their text book, during a testing situation is cheating.  If these items are found prior to the distribution of the test or quiz, it is considered “intent to cheat.”  The student will hand these items over and be allowed to take the test or quiz, but their grade will be lowered 10%.  If these items are found during the test or quiz, the student will receive a zero with no possibility of regaining any of those points.  They will also be referred to their counselor, the event noted on their permanent record and receive an N for citizenship.  The giving or receiving of information during a testing situation will have the same consequences listed above.

  2. 1.7 Difference Quotient, Absolute Value, Greatest Integer, & Piecewise Functions

  3. 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

  4. Ex 3) Graph for –3 ≤ x ≤ 3 y x

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

  6. 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

  7. Interval notation: • If you use infinity, always use open notation: • It is useful to know the intervals in which the graph in 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 closed: [a, b] open: (a, b) a a a a b b b b half-open: (a, b] [a, b) (goes up as you go to right) (goes down as you go to right)

  8. 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? y x Inc: (0, 1) Const: Yes!

  9. Homework #206 Pg 47 #3, 4, 6–8, 10, 12, 14–17, 19, 21–29 odd, 33, 41, 43

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