Read the summary and the most important questions on Business precalculus

• 1 Functions and lines

• 1.1.1 Function notation

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• Height is a funcation of age

  Means h is  f of a 
  h=f(a)
  h(a)

• 1.1.6 Evaluating and solving a graph

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• Solving a funcation equation using a graph

  Requires taking the given output and looking at the graph to determine the corresponding input

• 1.1.7 Formulas as functions

• Define(express) relationship using formulas

  Express the relationship 2n+6p=12 as a function p= f(n)
  
  soln:
  2n+6p=12
  2n-2n+6p=12-2n 
  6p=12-2n
  6p/6=12/6-2n/6
  p=f(n)= 2-2/3n

• 1.1.8 test of knowledge of all the topic dicuss in this section

• Example 12 given the funcation h(p)=p^2 +2pa) evlaute h(4)b) slove h(p)=3

  Slon 
  a) h(4)= p^2+2p
               = 4^2 +2(4)
               = 16  + 8
                = 24
  
  b) h(p)=3 
             3= p^2+2p
         -3+3=p^2 +2p-3
              0=P^2+2p-3
  factor it  x^2 -y^2= (x+y)(x-) so 
              0= (p-3)( p+1)
  
  then 0=p-3    & 0=p+1
            p=-3          p=1
                        
  check the answer 
  h(p)=p^2+2p
  3=-3^2+2(-3)
  3=9-6
  3=3

• 1.2.1 Notation

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• Notation 9 interval notation

  This is one way to describe intervals of input and output values, but it not the only way.
  
  other ways 
  

  • inequality
  •    set builder notation

• Inequlity, set buider notation, interval notaion

  The value of h is greater than 5 and less than or equal to 10

• To combine two intervals together, using inequalities or set-builder notation, w 

  We can use  the word or. In interval notation, we use the unione use the union symbol, U  to combine two concentrated intervals together 

• 1.2.2 Domain and Range from graph

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• Domain and range from grphs

  We can also talk about domain and range based on graphs

• 1.2.4 Piecewise funcations

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• Pice wise funcations example

   Example 5 and 6

• 1.2.5 Sketch a graph of the funcation

• Sketch a grpah of the funcation  ( piecewise funcations graph ) 

   There are 2 step 
  1. Draw each line apart 
  2. Combine all line together