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# CH10A&10B Alg 2 H

### Exponential Functions

b^1/n=? n√b
b^(m/n)=? n√b or (n√b)^m
Exponential Equation Variable appears in an exponent (no roots)
one-to-one function for every p and q in the domain of a function, f(p)=f(q) if and only if p=q.
Composite function The function whose value at x is f(g(x)). f and g are combined to produce the comspite: f(g(x))=(fog)(x)
Identify function Maps x to itself, f(x)=x or h(x)=x.
*Inverse function 2 functions are inverse if and only if f(g(x))=x and g(f(x))=x.
**a function has an inverse function if and only if...(2) it passes the horizontal line test; graphs are reflective over y=x
how to find the inverse fn switch x and y, and solve for y
general equation of an exponential function y-k=a(b)^(x-h)
what is the origin and horizontal asymptote? (h,k) and y=k
what base value indicates exponential decay or exponential growth? decay: 0<b<1 and growth: b>1
domain and range of an exponential function? D=all real #s R={y:y>k} (growth), and {y:y<k} (decay)
log function is... the inverse of an exponential function
**product property logb(MN)=logbM+logbN
**quotient property logb(M/N)=logbM-logbN
**power property logbM^k=k*logbM
**compound interest formula A=P(1+r/n)^nt A=amt accumulated, P=deposit (principal), r=interest rate (%), n=# of times compounded per year, t=time in years
**doubling-time growth formula N=N.(2)^(t/d) N=population currently, N.=initial value (when t=0)
**half-life decay formula N=N.(1/2)^(t/h) h=half life
**exponential growth y=a(1+r)^t (b>1)
**exponential decay y=a(1-r)^t (0<b<1)
*common log log10X
*natural log logeX
**properties of the natural log e^lnx=x, lne^x=x (inverses)
**e=? 2.718
**change of base formula logaX=logX/loga (base goes to the bottom!)
Created by: allyson.lee