Unit: Absolute Values 
                          NAME ___________________________ Per ________ 
          
          5/12                        5/13 PROJECT DUE!!!!!!          5/14-15                              5/16  
                                                                                                            
          Compound Inequalities       Absolute Values                 Inequalities and Word Problems       Graphing 
                                                                                                            
          HW: Part 1                  HW: Part 2                      HW:  Part 3                          HW:  Part 4  
                                       
          5/19                        5/20                            5/21-22 Senior Finals                5/23  Senior Finals 
                                                                                                            
          Review                      TEST: Absolute                  Everyone but seniors: Start Trig      
                                      Value Test                       
          HW:   Review 
                                       
          
         Objectives: 
         To graph absolute value equations and inequalities 
         To describe the transformations from the parent function 
         To determine the domain and range of an absolute value equation 
         To solve absolute value equations 
         To solve absolute value inequalities 
         To determine a reasonable solution to a real-world application 
         To solve compound inequalities 
          
         Pre-AP: To write an equation to model a real world application 
          
         Essential Questions: 
         When solving an absolute value equation or inequality, why do you have to solve it twice? 
         When do you have a disjunction or conjunction when solving an absolute value equation or inequality? 
         What is the difference between the two types of compound statements? 
         How do the transformations affect the domain, range, and vertex of the absolute value parent function? 
          
          
          
          
          
          
          
          
          
          
          
              Part 1 – Compound Inequalities 
              A _________________________ statement is made up of more than one equation or inequality.  
              A _________________________ is a compound statement that uses the word or.                                                                                     Dis- means “apart.” 
              A _________________________ is a compound statement that uses the word and.                                                                                    Disjunctions have two 
                                                                                                                                                                             separate pieces.  
                                                                                                                                                                             Con- means “together” 
                                                                                                                                                                             Conjunctions represent 
                    1)  6y < –24 OR y +5 ≥ 3                                                                                                                                 one piece. 
                                                                                                                                                                              
                                                                                                                               4)  – x + 2 < –1 OR 5x ≥ 30                                               
                                                                                                                         
                                                                                                                                                                                         
                                                                                                                         
                                                                                                                         
                                                                                                                         
                                                                                                                         
                    2)                                                                                                         5)  2x ≥ –6 AND –x > –4                                      
                                                                                                                         
                                                                                                                                                                                         
                                                                                                                         
                                                                                                                         
                                                                                                                         
                                                                                                                                                       x      7      1 1
                    3)  −64 < 6b − 4 < −22                                                                                     6)  PRE-AP  3  2  3 2 x
                                                                                                                         
                                                                                                                                                                                         
                                                                                                                         
               
               
               
               
              Part 2 – Absolute Values                                                                                                         Absolute-value equations and 
                                                                                                                                               inequalities can be 
                                                                                                                                               represented by compound 
                                                                                                                                               statements. 
                                                                                                                                         
               
              The solutions of |x| = 3 are the two points that are 3 units from zero. The solution is a disjunction: _________ 
                            
                    1)  |–3 + k| = 10   
                                                                                                                               2)                              
                                                                                                                                      
                                                                                                                                
                                                                                                                                      
                                                                                                                                      
           3)  3|x + 9| = 39                                      4)  |6x| – 8 = 22 
                                                                   
                                                                   
                                                                
                                                                
                                                                
        
        
       Part 2 – Inequalities 
        The solutions of |x| < 3 are the points that are less than 3 units from zero.  
       The solution is a conjunction: ______________________                                                
        
        
       The solutions of |x| > 3 are the points that are more than 3 units from zero.  
       The solution is a disjunction: ______________________                                                
        
        
        
        
        
        
           1)  |–4q + 2| ≥ 10              
                                                                  4)                               
                                                                       
                                                                                                        
                                                                       
                                                                       
                                                                       
           2)  |4x – 8| < 12                                           
                                                                  5)  |0.5r| – 3 ≥ –3              
                                                                       
                                                                                                        
                                                                       
                                                                       
                                                                       
                                                                       
           3)                                                     6)  |3x| + 36 > 12               
                                                                       
                                                                                                        
                                                                       
               
                                                                                         23x 
                                                                                   8)             1               
              7)                                                                            3
                                                                                                                                  
                                                                                         
                                                                                         
                   
                   
                   
                                                                                                              Hint: If you want within 
                                                                                                              the range, use <  If you 
         Word Problems with Inequalities  actual amt. - ideal amt. tolerance                                 want out of the range, 
                                                                                                              use > 
                                                                                                               
              9)   A manufacturer had a 0.3 oz tolerance for a bag of chips advertised as 4 oz. Write an inequality that 
                  would represent the acceptable volume for “4 oz” bags. Give a weight that would be acceptable and 
                  one that would not be acceptable.  
                   
                   
              10) A manufacturer has a tolerance of 0.36 lb for a bag of potting soil advertised as 9.6 lb.  Write and solve 
                  an absolute value inequality that describes unacceptable weights for “9.6 lb” bags. Give a weight that 
                  would be acceptable and one that would not be acceptable. 
                   
                   
                   
              11) PRE-AP    A survey of business managers reported that 87.6% read the newspaper. Results of this 
                  survey can be off by as much as 2.3 percentage points. Write an inequality that describes the actual 
                  percent of managers that read the newspaper, x.   
                   
                   
                   
         Part 3 – Graphs from the Parent Function 
                                    
         General                                     Parent Function 
          y a xh k                                           yx
                                                                            
         a:                                                 X      Y 
                                                                    
         h:                                                         
                                                                    
                                                                    
         k:                                                         
          
         Domain:                                       Domain: 
         Range:                                       Range: