Assignment, pencil, red pen, highlighter, textbook, GP notebook, calculator Complete the tables and write the rule for each of the following sequences. 1) The sequence is arithmetic. 2) The sequence is geometric. n 0 1 2 3 4 n 0 1 2 t(n) 15 13 11 9 7 t(n) 4 12 36 +2 d 11 7 4 2 2 4 2 +2 t(n) = b(m)n t(n) 2n 15 t(n) = 4(3)n +2 +2 total: 12 4 108 324 m +1 +1 3 m 324 = 36 m m 324 = 36(m)2 +1 36 36 9 = (m)2 9= m2 3 = m +1 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) Set Notation Vs. { x | –2 < x 5 } { x | 10 < x < } {x|x0} {x|x=9} Interval Notation ( –2, 5 ] (10, ) (–, 0) U (0, ) [ 9] Let’s try the first few problems on today’s worksheet. Domain, Range, & Functions Worksheet y 1. 10 –5 y 2. 5 –10 x 3. 10 –5 5 –10 x y 10 –5 5 –10 D: (set notation) {x| –1 < x ≤ 3} {x| –3 ≤ x ≤ 5} {x| –5 < x < 3} (–1, 3] D: (interval) R: (set notation) {y| –7 ≤ y < 6} [–7, 6) R: (interval) [–3, 5] {y| –5 ≤ y ≤ 8} [–5, 8] (–5, 3) {y| –2 < y ≤ 9} (–2, 9] x 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 2 x 6 10 3 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. 2 x 6 10 3 2 3 x 36 310 3 2x 18 30 2x 12 x6 Multiply everything by 3. Simplify and solve Fraction Busters Now for two more challenging examples. . . 1) x 2x 5 6 3 x 2 2 x 6 6 65 6 3 x 4x 30 5x 30 x6 2) 6 3 1 x 4 6 3 4 x 4 x 4 x1 x 4 24 3x 4x 24 x 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/SetBu ilderNotation.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_ht ml/160W1-3S05.pdf 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. { 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 The set of all than or equal to 5 “such that” real numbers x {x|x0} 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. x 1) -3 -2 -1 0 1 2 3 4 5 6 7 8 Set builder: {x | –3 < x ≤ 5 } ( –3, 5 ] Interval: 2) x -3 -2 -1 0 1 2 3 4 5 6 7 8 Set builder: {x | 1 ≤ x < } Interval: [ 1, ) x 3) -3 -2 -1 0 Set builder: {x | – < x < } Interval: ( –, ) 1 2 3 4 5 6 7 8