1.FUNCTIONS

1.FUNCTIONS

1. asymptotes

   • never reach
     • horizontal
     • vertical
     • oblique

2. exponential functions

   • at least 7 numbers
   • relation between (y) and (x)
   • y(x)=b^x
   • applications
     • depreciation
       • lost value
         • over time
         • Vf=Vo(1-dr)^t
           • vf=final value
           • vo= initial value
           • dr=depreciation value
           • t=time
     • compound interest
       • earning
         • A=P(1+r/n)^tn
           • t= time
           • P=initial amount
           • R=rate
           • n=period
     • half-life
       • radioactive decay
       • Q=Qo(1/2)t/h
         • Q=final amount value
         • Qo= final amount
         • T= time
         • h=half-life
     • continuously compound
       • interest keeps earning
       • principal is continuously earning
       • A=Pe^rt
         • P=principal
         • R=rate
         • T=time in years
         • e=euler's number
           • 2.718
     • exponential growth
       • increases
       • y(t)=a x e^kt
         • t=time
         • k=rate of growth
         • e= euler's number
     • exponential decay
       • decreases
       • y(t)=a x e^kt
         • k=rate of decay

3. logarithms

   • way to find exponent
   • 1. log_b (mxp)=log_bm+log_bP
   • 4.log with same base and product
     • equals the same number
   • 3.log=_bb=1
   • 4. log_22^3=3
   • 5.log_5-1=0
   • 6.10log_10^100=10^2

4. composing functions

   • FoG(x)=f(g(x))
   • combining functions
     • F(x)+G(x)
     • F(x)-G(x)
     • F(x) x G(x)
     • F(x) / G(x)
   • inverse functions
     • 1. F(x) with y
     • 2. interchange X and Y
     • 3. solve the equation
     • 4. y with F-1(x)

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