Pre-Calc FInal

How do you point out a function?

When there is one output value for every x-value

How to determine the domain of a function?

set denominator of action equal to zero

2 RULES

1. anything divided by zero is undefined

2. negative in a square root

when writing parentheses

the lower number always goes first!

cosine

adjacent/hypotenuse

Sine

opposite/hypotenuse

Tangent

Oppisite/ adjacent

csc

hyp/op

Secant

hyp/adjacent

Cotangent

adjacent/oppisite

Isosceles Triangle

When finding angles on Unit Circle CSC, SEC, COT

csc→1/Y

sec→ 1/x

Cot→ x/y

(x,y)→ are your coordinates!!

a^2+b^2=c^2

c^2 is always your hypotenuse

Remember !!

no square roots on denominator!

Compound Interest Formula!

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

\
\
P=Principe balence

r= interest rate

n= number of times interest applied per time period

t= number of time periods elapsed

\

What do you do for a Quadratic Function

\-Add to middle

\-Multiply to end

Slope Intercept form

y=mx+b

m=slope

x=variable

b=y-intercept

y=variable

Slope

rise/run

* y2-y2/x2-x1

Quadrents

numbered counter-clock wise area contained by the x &y axis

x&y plane

plane they form at intersection

Cordinate axis’s

2 fixed coordinate lines that form the cordinate plane

\

origin

2 lines point of intersection

Quadrents

Counter clock wise

\
2 1

34

Distance Formula

√\[(x₂ - x₁)² + (y₂ - y₁)²\].

Mid Point Formula

f (x)

F is a machine creating y out of X

Functions →

can only have One output value for every input value!

When Square root is already present in a function

only one version is necessary

When using square root as a solving technique

both + and -

Bracket \[=

included

Parenthesis (=

Excluded

IDENTITY FUNCTION y=-f(x)

x-axis reflection making y-negative

IDENTITY FUNCTION y=f(-x)

y-axis reflection

\-making x negative

Notation→ (fog)(x)

F(g(x)

\
“f of g of x”

if you have 2 x-values

you do the domain for both

Quadratic Function standard form

f(x) = ax2 + bx + c

→ a cannot equal 0

→ b, c can be anything!!

Quadratic Formula for x-intercepts

How to solve for vertex?

x=-b/2a

if in standard form and leading coefficient is postive=

opens up

\

If leading coefficient is negative and in standard form =

opens down

Steps in solving a Quadratic Equation

1. Opens up/down

2. X-intercepts set equation = to zero

3. Y-intercept , set x=0

4. Factoring

Exponents both (+) or (-)

→ touches (Bounces)

Opposite

crosses x-axis

x-intercepts

where x=o

Multiplicity even→

graph bounces off x-axis

Multiplicity odd→

graph crosses x-axis

huge/tiny=

normal/tiny=

HUGE

normal/huge=

Still really tiny

tiny/tiny

could be tiny, normal or huge

Whats an asymptote?

a line or a curve that a function goes close to and might NEVER touch

Aysmptotes do NOT ..

X-axis

Rational Functions

a function defined as the quotient (division) of two polynomials

Asmpytotes may..

never be touched or be crossed by a function

Asymptotes of Polynomials

standard form

In order to solve for vertical asymptotes

set denominator equal to zero

How do you get a hole!

cancels out completely

How to find horizontal asymptotes

1. if top is heavy there is no horizontal asymptote

2. If the exponents are the same then divide both number

3. If bottom is heavy then it is zero

Rational functions.

x- intercept →numerator

domain→ denominator

Orignial formula (Continious compounding interest formula)

P(t)=Pe^rt

p=principal

e= e on calculator

r= rate of interest

t=time in years

y=log a ^x

form

Exponential Form

base^exponent= result

\
a^t=R

Logarithmic form

Degree to radians →

x pie/180

Radioans to Pie→

x 180/pie

For a Rational Function. intruder to find x-intercepts

set numerator equal to zero