appc (some) rules review

(rational functions ax^n/bx^d) n=d

lim→ a/b

(rational functions ax^n/bx^d) n<d

lim→ 0

(rational functions ax^n/bx^d) n>d

lim → a/bx^n-d , or slant asymptote when difference is equal to 1; use synthetic division

(rational functions ax^n/bx^d) multiplicity n>d

zero occurs

(rational functions ax^n/bx^d) multiplicity d>n

VA occurs

(rational functions ax^n/bx^d) multiplicities n=d

hole occurs

b^a=c

log_b c= a

aroc equation

y2-y1=m(x2-x1), slope y=mx+b

amplitude

max-min/2

midline

max+min/2

range of sin cos tan

[-1,1]

angle measures of arcsin, arctan

(-pi/2, pi/2)

angle measure of arccos

(0, pi)

zeros of tan=

zeros of sin

zeros of cos= (in tan=sin/cos)

VA

tan (3Ø)= pi/2+pi K

tan(Ø)= 1/3[pi/2 + pi k]

tan(Ø)= pi/6 + pi/3 k

sin=

cos(Ø-pi/2)

cos=

sin(Ø+pi/2)

f(x)= a sin/cos (b(x+c))+d → a=

amplitude, vertical dilation

f(x)= a sin/cos (b(x+c))+d → b=

horizontal dilation, period= 2pi/b

f(x)= a sin/cos (b(x+c))+d → c=

horizontal translation; phase shift

f(x)= a sin/cos (b(x+c))+d → d

vertical translation, affects midline

sin function (starting/check points)

midline, max, mid, min, mid

cos function (starting/check points)

max, mid, min, mid, max

cos(2Ø)

cos²Ø-sin²Ø

sin(2Ø)

2sinØcosØ