Assignment, pencil, red pen, highlighter, textbook, GP notebook, calculator U2D10 Have Out: Bellwork: Complete the tables and write the rule for each of the following sequences. 1) The sequence is arithmetic. 2) The sequence is geometric. n 1 2 3 4 t(n) 11 7 n 1 2 3 4 t(n) 36 324 15 13 9 4 12 108 +2 +2 m m +1 +1 t(n) = b(m)n 324 = 36 m m 324 = 36(m)2 +1 36 t(n) = 4(3)n +2 9 = (m)2 total: +2 +1 3 = m

Interval Notation Examples: Add to your notes. Interval notation can be a more efficient way of expressing domain and range. Interval notation uses the following symbols: Symbol Represents U The union of two or more sets ( ) An open interval (i.e., do not include the endpoints) [ ] A closed interval (i.e., include the endpoints) Examples: Set Notation Vs. Interval Notation { x | –2 < x  5 } ( –2, 5 ] { x | 10 < x <  } ( 10,  ) { x | x  0 } (–, 0) U (0, ) { x | x = 9 } [ 9 ]

Let’s try the first few problems on today’s worksheet.

Domain, Range, & Functions Worksheet y y y 1. 2. 3. 10 10 10 x x x –5 5 –5 5 –5 5 –10 –10 –10 D: (set notation) {x| –1 < x ≤ 3} {x| –3 ≤ x ≤ 5} {x| –5 < x < 3} D: (interval) (–1, 3] [–3, 5] (–5, 3) {y| –7 ≤ y < 6} {y| –5 ≤ y ≤ 8} {y| –2 < y ≤ 9} R: (set notation) [–7, 6) [–5, 8] (–2, 9] R: (interval)

How many of you like working with fractions??? Now, we are going to work with How many of you like working with fractions??? Suppose there was a way to eliminate fractions from an equation that you are trying to solve. Wouldn’t that make it easier to do??? This is known as Fraction Busters

Fraction Busters Summarize in your notes To rewrite this equation without the fraction, we ask ourselves , “How can we eliminate the three?” Fraction Busters uses the Multiplication Property of Equality (that is we can multiply both sides of the equation by the same number and still maintain equality) to rewrite the equation without the fraction. Start by multiplying the 3 with EVERYTHING on BOTH SIDES of the equation.

Fraction Busters Summarize in your notes Multiply everything by 3. Simplify and solve

Fraction Busters Now for two more challenging examples. . . 1) 2) 2

Clear your desk except for pencil, highlighter, and a calculator! It's Quiz Time! Clear your desk except for pencil, highlighter, and a calculator! After the quiz, work on the worksheet.

Old Slides

Resources http://cnx.org/content/m13596/latest/ http://www.biology.arizona.edu/biomath/tutorials/Notation/SetBuilderNotation.html http://www.analyzemath.com/DomainRange/DomainRange.html http://www.phsmath.org/Alg1/pdfs/Lessons/L82.84.87.pdf http://www.montgomerycollege.edu/faculty/~jriseber/public_html/160W1-3S05.pdf

Set Builder Notation Example #1: Example #2: Recall: Don’t copy… The notation that we have been using for domain and range is called set builder notation. In this notation, curly parentheses and variables are used to express domain and range. Example #1: { x | –2 < x  5 } means “the set of all real numbers x such that x is greater than –2 and less than or equal to 5.” x is greater than –2 and less than or equal to 5 The set of all real numbers x “such that” Example #2: { x | x  0 } Means “the set of all real numbers x such that x is not equal to zero.”

Find the domain using set builder notation and interval notation. Examples: 1) x -3 -2 -1 1 2 3 4 5 6 7 8 Set builder:  {x | } –3 < x ≤ 5 ( –3, 5 ] Interval: 2) x -3 -2 -1 1 2 3 4 5 6 7 8  {x | } ≤ x  Set builder: 1 < Interval:  [   1, ) 3) x -3 -2 -1 1 2 3 4 5 6 7 8 Set builder:  {x | } – < x  < Interval: ( –,  )