Unit 5 ACP Pre-Calc

a function with domain and range is a one to one function when....

Whenever a≠b in domain, then f(a)≠f(b) in range

Whenever f(a)=f(b) in range, then a=b in domain

horizontal line test

test used to determine if a function is 1-1, function is 1-1 only if every horizontal line intersects graph of f at only one point

inverse function

A function g with domain R and range D is the inverse function of f, provided the following condition is true for every x in D and every y in R

[ y=f(x) if and only if x=g(y) ]

how to solve inverse functions

Step 1: is it 1-1?

Step 2: Switch and solve

Compound interest formula

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

Where P=initial value

r=rate

n=number of interest periods per year

t=number of years P is invested

A= amount after t years

continuously compounded interest

A=Pe^rt

Where P= initial

r=rate

t=number of years P is invested

A= amount after t years

Law of growth/decay formula

q=q0e^rt

Where positive r is the rate of growth (or negative r is the rate of decay) for q

Note:

Exponentials and logs are inverses of each other and are both 1-1 functions

Common log and natural log

log x = log10 x

In x = log e X

Properties of Logs

Log(AB)=LogA+LogB

Log(A/B)=LogA-LogB

LogA^p=PLogA—useful when solving unknowing exponent

Note:

When solving logs, the coefficient in front has to be 1 to solve in exponent form

Note:

Take natural log of both sides when x is exponent and you're trying to solve for x