Summary: Business Precalculus
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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 givenoutput and looking at thegraph to determine thecorresponding 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
2n2n+6p=122n
6p=122n
6p/6=12/62n/6
p=f(n)= 22/3n 
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 +2p3
0=P^2+2p3
factor it x^2 y^2= (x+y)(x) so
0= (p3)( p+1)
then 0=p3 & 0=p+1
p=3 p=1
check the answer
h(p)=p^2+2p
3=3^2+2(3)
3=96
3=3 
1.2.1 Notation
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Notation 9 interval notation
This isone way todescribe intervals ofinput andoutput 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 setbuilder notation, w
We can use the word or. Ininterval notation , we use theunione 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
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