Section+3.1

Section 3.1 Exponential and Logistic Functions

Exponential Function - f(x) = a*b^x where a is not equal to 0, b>0, b is not equal to 1 "a" is the initial zero "b" is the base

Two Types: Exponential Growth: b>1 Exponential Decay: 0<b<1

Graphing For graphing the parent function is f(x) = 2^x Properties: y-int = (0,a) Horizontal asymptote at y=0 Domain: all real numbers Range: (0,∞) one-to-one function

Reflections: f(x) = a*b^(x-h) + K a: vertical stretch or shrink, -a: reflection over x-axis b: growth or decay h: shifts left(+h) or right(-h) k: shifts up(+k) or down(-k)

Logistic Function: Restricted growth: bounded above and below

Let a,b,c,k be positive, b<1 f(x) = c/(1+ a*b^x) or f(x) = c/(1+a*e^-x)

horizontal asymptotes are y=0, y=c Range: (o,c) Domain: all real numbers