Studied by 39 peopleHow 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
anything divided by zero is undefined
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
Opens up/down
X-intercepts set equation = to zero
Y-intercept , set x=0
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
if top is heavy there is no horizontal asymptote
If the exponents are the same then divide both number
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
Note
Flashcard