exponential functions

Exponential function

The variable is the exponent

What is the build of exponential functions?

f(x) = a(b^x)

What do exponential functions show?

Exponential growth or decay

Exponential growth

when a>0 and b>1

Exponential decay

When a>0 and between 0 and 1

Horizontal asymptote

A horizontal line that a graph approaches but never reaches as input values approach positive or negative infinity

Always increasing or decreasing

Exponential function

graph of f(x) = b^x will always have a y intercept of

(0,1)

The graph of f(x) =b^x will always contain the point

(1,b)

in f(x) = a(b^x) , the y intercept is

(0,a)

The graph of f(x) = a(b^x) must include

(1,ab)