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(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
Note
Flashcard