Four
ways to represent afunction Definitions:
Function, Domain and Range of (Polynomial of first and second degree), Representation of Functions and their Graphs, The Vertical Line
Test, Piecewise Defined Functions, Symmetry (Odd & Even) Functions.
Mathematical Models:
A Catalog of Essential Functions Essential Functions:
Polynomial, Power, Rational, Algebraic, Trigonometric,
Exponential, and Logarithmic. Families of Essential
Functions and Their Graphs.(must know)
New Functions from
Old Functions Transformations of
Functions: i) Vertical and Horizontal Shifts. ii) Vertical and Horizontal Reflecting, Combination of Functions (f(+,-)g), f.g, f/g, And Composite Functions) and their Domains
Inverse Functions and Logarithms Inverse Functions:
Definitions Horizontal Line Test; Logarithmic
Functions: Definitions Laws of Logarithms, Natural Logarithm:
formulas Inverse Trigonometric
Functions and their cancellation equations: (𝐲 =
𝐬𝐢𝐧−𝟏𝐱,
𝐲=
𝐜𝐨𝐬−𝟏𝐱,
𝐲
= 𝐭𝐚𝐧−𝟏𝐱
only), Identify the graphs of a function and it’s
inverse if they are given on the same axes.
The Limits of a
Function Finding Limits
Numerically and Graphically One-Sided Limits How can a Limits Fail to Exist?; Infinite Limits:
(Vertical Asymptotes),
Calculating Limits
Using the
Limits Laws Properties of Limits:
The Limits Laws Evaluating Limits by
Direct Substitution
Property; Using One-Sided Limits The Squeezed Theorem
Derivative of
Polynomials &
Exponential Functions Constant Functions,
Power Functions Definition of normal line New
Derivatives from Old Exponential Function
what Derivatives Tell
Us about the Shape of a Graph What Does 𝒇′
Say About 𝒇?
Increasing/Decreasing
Test The First Derivative
Test What Does 𝒇′′
Say About 𝒇?
Concavity
Test Inflection Point
