207
First Day Handout for Students
MATH 2412
Precalculus: Functions and Graphs
Spring 12
Meets: TTh 10:55am- 12:40pm
RVS A - 2212
Instructor: Rene Lumampao
Phone: (512) 223-6295
Email address: [email protected]
You will be able to access the lecture n
Chapter 10
Compositions, Inverses, and
Combinations of Functions
10.1 Composition of Functions
Key Points
Finding the composition of two functions
numerically, graphically and symbolically
Interpreting the composition of two
functions
Decomposing a fun
Chapter 9
Trigonometric Identities and Their
Applications
9.1 Identities, Expressions and
Equations
Key Points
The difference between an equation and
an identity
The Pythagorean and double angle
identities
Identities (8, 16)
Pythagorean
sin 2 + cos 2 =
Chapter 7
Trigonometry in Circles and
Triangles
7.3 Graphs of the sine and
Cosine
Key Points
Graphing y = Asin(t) and y = Acos(t)
Graphing y = sin(t) + k and y = cos(t) + k
Amplitude, period, and midline
Using Angles to Measure
Position On a Circle
Con
Chapter 6
Transformations of Functions and
Their Graphs
6.1 Vertical and Horizontal
Shifts
Key Points
Horizontal and vertical graphical shifts
Finding a formula for a shifted graph in
terms of the formula for the original graph
The graphs of many functi
Skills Refresher Ch. 5 pg. 219
Logarithms
Chapter 5
Logarithmic Functions
5.1 LOGARITHMS AND THEIR
PROPERTIES
Key Points
Using logarithms to solve exponential
equations
The definition of the logarithm function
The equivalence of exponential and
logarit
Skills Refresher for Chapter 4
Exponents
Example
Simplify each expression by hand.
a) 82/3
b) (32)4/5
Pg. 177
36,44,48,50,52,54
Chapter 4
Exponential Functions
4.1 Introduction to The Family of
Exponential Functions
Key Points
Growth factors and growth r
Chapter 3
Quadratic Functions
3.1 Introduction to the Family of
Quadratic Functions
Key Points
The general formula for quadratic functions
Finding the zeros of a quadratic function
Finding the Zeros of a Quadratic
Function
Example
Find the zeros of f(x)
Chapter 2
Functions
2.1 Input and Output
Key Points
Basic function interpretation and
manipulation using standard function
notation
Finding Output Values:
Evaluating a Function
Example
Let h(x) = x2 + 2x - 4. Evaluate and simplify the
following expressio
Chapter 1
Linear Functions and Change
1.1 Functions and function
notation
Key Points
The definition of a function
Numerical, graphical, symbolic, and verbal
representaions
The vertical line test
Basic function concepts and language
f ( x) = x 2
f ( x)
Chapter 12
Vectors
12.1 Vectors
Key Points
The definition of displacement
Physical quantities represented by vectors
Addition and subtraction of vectors
geometrically
Scalar multiplication
The magnitude of a vector
Vectors
Many physical quantities ad
Chapter 11
Polynomials and Rational
Functions
11.1 Power functions
Key Points
Proportionality and power functions
The general form of a power function
The classification of power functions into
six basic types
f ( x ) = kx p
Power function
f ( x) = kx
Review for Exam 2
PreCalculus
You are responsible to know all of the formulas required for the exam. I have included
additional practice problems for you to review for your exam, but make sure that you go
over your homework and notes when preparing for th
Review for Exam 1
PreCalculus
You are responsible to know all of the formulas required for the exam. I have included
additional practice problems for you to review for your exam, but make sure that you go
over your homework and notes when preparing for th
Chapter 14
Parametric Equations and Conic
Sections
14.1 Parametric Equations
Parametric Equations of a Plane
Curve
A plane curve is a set of points (x, y) such
that x = f(t), y = g(t), and f and g are both
defined on an interval I. The equations x =
f(t)
Chapter 13
Sequences and Series
13.1 Sequences
Key Points
Definition of a sequence
Arithmetic and geometric sequences
Sequences
Examples
Finite infinite
Notation
Notation for Sequences and Examples
We denote the terms of a sequence by
a1, a2, a3, . .
Chapter 8
The Trigonometric Functions
8.2 Sinusoidal Functions and
Their Graphs
Key Points
Graphing y = Asin(B(t h) + k and
y = Acos(B(t h) + k
Amplitude, period, frequency and
horizontal shift
Finding formulas for periodic functions
using sine and co