Unit 1 AP Precalculus

Unit 1 - Polynomial and Rational Functions

Increasing

Positive ROC

Decreasing

Negative ROC

Concave Up

ROC is increasing

Concave Down

ROC is decreasing

Point of Inflection

ROC changes from inc. to dec. or dec. to inc.

Key phrase when justifying

over equal-length input-value intervals

AROC

f(b) - f(a) / b - a

Odd Function

f(-x) = -f(x)

Even Function

f(-x) = f(x)

Y-intercept

x = 0

X-intercept

y = 0

Multiplicity - factor of 1

travels through linearly

Multiplicity - factor of 2

bounds qudratically

Multiplicity - factor of 3

bends cubically

Odd Degree

end behaviors disagree

Even Degree

end behaviors agree

Complex Conjugate

if (a+bi) is a factor then (a-bi) is also a factor

Binomial Expansion

use pascal’s triangle

Transformations (a)

possible vertical reflection and/or dilation by a factor of a

Transformations (b)

possible horizontal reflection and/or dilation by a factor of 1/b

Transformations (c or h)

possible horizontal translation in the direction (-)c/h

Transformations (d or k)

possible vertical translation in the direction k

Table Identification - Linear

both input and output change consistently

Table Identification - Quadratic

input changes consistently and 2nd differences of output =

Table Identification - Cubic

input values changes consistently and 3rd differences of output =

Table Identification - Exponential

input changes consistently/output changes proportionately

Table Identification - Logarithmic

input changes proportionately/output changes consistently

Solving Inequalities

1. Consider Domain Restrictions

2. Solve and use all critical values to test around

3. Determine intervals of positivity and/or negativity

Vertical Asymptote

n/0 and lim_{x→ a} r(x) = ± infinity

Horizontal Asymptote

lim_x→± r(x) = b

Hole

0/0 lim_x→c r(x) = L

Residual

Actual Value (from Data) minus Predicted Value (from Model)