Precalc Green Sheets Unit 1 - Polynomial & Rational Functions

sin (a+-b)

sin a cos a +- cos b sin b

cos (a+b)

cos(a-b)

think opposite sign, cos cos sin sin

ex. for cos (a+b)

• cos a cos b - sin a sin b

how to find θ

θ=s/r

s = arc length

BOBO - bigger on bottom 0

HA at y=0

BETC - same degree

Ratio of leading coefficients = HA (y=ratio)

BOTU - bigger on top

slant asymptote

• leading coefficients + x’s on bottom and top, reduce x’s

Vertical asymptotes in rational functions

factor left in the denominator = VA

• if a hole occurs as well, the hole just occurs inside the VA.

• VA takes precedence

residual = actual - predicted (model)

pattern = NOT appropriate

• Neg residual = overestimate

• Pos residual = underestimate

exponential growth

growing away from 0

exponential decay

coming to 0

exponentials

• always inc or dec

• end behavior → neg inf, pos inf, or 0, ONE SIDE will be 0