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hint

1

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

lim→ a/b

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2

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

lim→ 0

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3

(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

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4

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

zero occurs

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5

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

VA occurs

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6

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

hole occurs

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7

b^a=c

log_b c= a

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8

aroc equation

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

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9

amplitude

max-min/2

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10

midline

max+min/2

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11

range of sin cos tan

[-1,1]

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12

angle measures of arcsin, arctan

(-pi/2, pi/2)

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13

angle measure of arccos

(0, pi)

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14

zeros of tan=

zeros of sin

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15

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

VA

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16

tan (3Ø)= pi/2+pi K

tan(Ø)= 1/3[pi/2 + pi k]

tan(Ø)= pi/6 + pi/3 k

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17

sin=

cos(Ø-pi/2)

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18

cos=

sin(Ø+pi/2)

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19

f(x)= a sin/cos (b(x+c))+d → a=

amplitude, vertical dilation

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20

f(x)= a sin/cos (b(x+c))+d → b=

horizontal dilation, period= 2pi/b

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21

f(x)= a sin/cos (b(x+c))+d → c=

horizontal translation; phase shift

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22

f(x)= a sin/cos (b(x+c))+d → d

vertical translation, affects midline

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23

sin function (starting/check points)

midline, max, mid, min, mid

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24

cos function (starting/check points)

max, mid, min, mid, max

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25

cos(2Ø)

cos²Ø-sin²Ø

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26

sin(2Ø)

2sinØcosØ

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