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Base

the number that is written with an exponent

exponent

A mathematical notation indicating the number of times a quantity is multiplied by itself

power

a number produced by raising a base to an exponent

Domain

The ______________________ is all the possible INPUT, X, values.

Range

The difference between the greatest number and the least number in a set of data.

Exponential Function

y = ab^x

logarithmic function

the inverse of the exponential function

common logarithms

The logarithm with base 10 is called the common logarithm and is denoted by omitting the base

log

abbreviation of common logarithms

natural logarithms

logarithmic functions of base e

e

Eulers number.

increasing function

a function whose graph increases as the values of the domain increase

decreasing functions

a function whose graph decreases as the values of the domain increase

constant function

a functions whose graph stays horizontal as the values of the domain increase

y-intercept

the point where the line crosses the y-axis

inverse relation

the relation that reverses each ordered pair (a,b) to (b,a)

one to one function

a function that has an inverse that is also a function

Horizontal Line Test

inverse of a function is also a function if and only if no horizontal line intersects more than one

log(b)1

0

log(b)b

1

log(b)b^x

x

b^log(b)x

x

log1

0

log10

1

log10^x

x

10^logx

x

ln1

0

lne

1

lne^x

x

e^lnx

x

log(b)N+log(b)M

The Product Rule: log(b)(MN)

log(b)N-log(b)M

The Quotient Rule: log(b)(M/N)

plog(b)M

The Power Rule: log(b)M^p

logM/logb

Change of Base (common logs): log(b)M

lnM/lnb

Change of Base (natural logs): log(b)M

F(x)=b^x

The exponential function with base b

f(x)=e^x

(Steeper Exponential Growth)

A=P(1+r/n)^(nt)

Formula for interest compounded n times per year

A=Pe^(rt)

Investment total under continuously compounded interest; A=...

log(b)x=y

Express in logarithmic form: y=b^x

y=b^x

Express in exponential form: log(b)x=y

e

An irrational number called the natural base

Describe the transformation f(x)=b^(x)+c

Shifts the graph c units upward

Describe the transformation f(x)=b^(x)-c

Shifts the graph c units downward

Describe the transformation f(x)=-b^x

Reflects the graph about the x-axis

Describe the transformation f(x)=b^(-x)

Reflects the graph about the y-axis

Vertical Stretch c>1

Describe the transformation f(x)=cb^x