All math

parent function of decay and exponential decay

f(x)=b^x

domain, range, an horizontal asymptote of expoenential decay/growth

domain: (-infinity, infinity). range (0, infinity) ha (y=0)

in f(x)= ab^x what is a,b, and x

a is inital value (y int (0,a)), b tells if its growth or decay, and x is input

growth interval for b

b>1

decay interval for b

0<b<1

to find decrease for decay do

1-b

to find increase in growth to

b-1

growth

y=a(1+r)^t

decay

y=a(1-r)^t

decay/growth factor in models is

inside the parenthesis (1 ± r)

if t is smth like t/28 you can

seperate it into ( (number) ^1/28)) t and solve

compound interest is a

growth function

compound interest formula

a=P(1+r/n)^nt or amount=principal (1+rate/number you compound) time

e is around

2.718

e can have a

neg exponent

natural base exponential function

y=ae^rx

if r in exponential natural base is r>0

then its growth (y=e^x)

if r in exponential natural base is r<0

thne its decay (y=e^-x(

continuisly compounded equation

a=Pe^rt

logb(n)=x

b^x=n

natural logartithm

lnx

graph of exp functions never touch

the asymptote

on both sides of exp. graph there are

arrows

horizontal translations

up in the exp

vertical translations

are belwo after the exp

in log e functions, asy

is x=

in normal exp functions asy

is y=

invefse of exp function is

log function

if log b ^x +1 then (not in paranethsis)

b^n=x +1

if log b(x+4) (in parenthesis)

b^n=(x+4)

logb ^mn

logb^m+logb^n

logb^(m/n)

logb^m-logb^n

log b^m^n

nlogb^m

condense only when

same base

chang =e of base formula

logc^a = log10^a/log10^c

answer of solving exp equations is in

curly bracket

in log rquations always check

solution

in log equations, pos answer is , neg answer is

true, false

when graphing exp functions graph

at least 3 points and asy

if base is same and a^x=a^b

x=b

when solving exp equations, do

everything to both sides

horizontal translations in log is always

in paranthesies

vertifcal translations in log are always

not in parenthesis

asy is affected by

vertical translation

asy in log is

inside (+a)

asy in exp is

outside ( )+a

exp fucntions equatins

f(x)=ab^x-h +k

log function

a logb ^ (x-h) +k

What phrase is sued to remember identities

SOH-CAH-TOA

(soh-cah toa (sct)) sin

opp/hyp

sct csc

hyp/opp

sct cos

adj/hyp

sct SEC

hyp/adj

sct TAN

opp/adj

sct COT

adj/opp

refrence angles used to

find trig functions of any angle

theta prime is always

positive and acute

steps to get a reference angle

1. draw angle, 2. create right triangle 3. use theta prime (inside) 4. pos/neg

deg to rad

deg times pi/180

rad to deg

rad times 180/pi

to find coterminal angles

add/subtract multiples of 360/2pi

sin graphing equation

f(x)=(a)sin(bx-h)+k

cos graphing equation

f(x)=a(cos)(bx-h)+k

what are things you need to graph during sin/cos (things you need to find)

amplitude, interval s (one cycle), centerline, endpoints

how do you find amplitdues

|a|

how do you find period

2pi/|b|

how to find intervals (one cycle)

(2pi/|b|)/4

centerline

y=k

endpoints

bx-h=0 and bx-h=2pi

how does a sin graph look/act

starts at center → moves to max

how does a cos graph move/act

starts at max and moves to center line

identies sin theta

1/csc(theta)

identites csc theta

1/sintheta

identites cos theta

1/sectheta

identites sec theta

1/costheta

tan theta identity

1/cot theta

cot theta identity

1/tan theta

tan theta idenity (2nd)

sintheta/costheta

cot theta identity 2

cos theta/ sin theta

sin² theta + cos ² theta equals

1

unit circle points

(1,0) (0,1) (-1,0) (0,-1)

radius of unit circle

r=1

degrees and radians of unit circle

0/2pi and 0/360 degrees, pi/2 and 90 degrees pi and 180 degrees, 3pi/2 and 270 degrees

order of sin, tan, cos, all for unit circle

ASTC (all students take calculus)

sin theta is equal to what coordinate in unit cirlce

y

cos theta is equal to what coordinate in unit circle

x

tan theta is equal to waht coordinate in the unit circle

y/x

60 degrees in raidans

pi/3

30 degrees in radians

pi/6

90 degrees in radians

pi/2

30-60-90 degree triangle side rules

x, 2x, and x square root of 3

45-45-90 degree triangle rules

x,x, and x square root of 2

in whole unit circle, interval between degrees is

ex: 0 to 30 to 45 to 60 to 90 (intervals: 30, 15, 15, 30)

in unit circle opp of 30 degress in a triangle is always

½

in unit cirlce the side touching 60 degrees in a triangle is always

shorter and equal to x

every 30 degreees in unit circle is

pi/6 per (can also simplify to pi/3) (for 30 60 90 etc degrees)

every 45 degrees in unit circle is

pi/4 per (for 45,90, 135 degrees etc)

cheat code for unit circle radians

quadratn one: its always 1/3,4,6 quadrant 2: one less than demoninator 3: one more than denominatiro 4: x2 -1 denominator