Pre Calculus

Pre Calculus

1. Functions

   • Transformations
     • Vertical Transformations
       • Shifts
         • g(x)=f(x)+k
         • Dilations and Reflection
           • if a > 1, the the graph will be stretch
             • g(x)=2f(x)
           • If 0<a<1, the the graph will be compressed
             • g(x)=0.5f(x)
           • if a<0, then there will be a vertical reflection.
     • Horizontal Transformations
       • Shifts
         • Dilations and Reflection
           • If b>1, then the graph will be compressed by 1/b.
             • g(x)=f(0.5x)
           • If 0<b<1, then the graph will be stretched by 1/b.
             • g(x)=f(2x)
           • If b<0, then there will be a horizontal reflection
         • g(x)=f(x+k)
   • Representing a Function
     • Graphically
     • Enumeratively
     • Verbally
     • Algebraically
   • Catalog of Functions
   • Linear Functions
     • Average Rate of Change
       • f(x_2) - f(x_1) / x_2 - x_1
     • y=mx+b
       • Perpendicular
         • f(x)=4x+5 / g(x)=-1/4 -7
         • parallel
           • f(x)=-2x+6 / g(x)=-2x-4

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