Chapters:

Section 1.1: Functions and Function Notations.

Section 1.1.pdf

Learning objectives are

• Various presentations and notations of functions
• Vertical line test
• Evaluating functions using their algebraic rules

Solving Equations.

Group Work 1.pdf (Solution Will Only Be Provided on The Course Canvas.)

Section 1.2: Domain and Range.

Section 1.2.pdf
A Geogebra App

Learning objectives are

• Domain and range of rational and radical functions
• Piecewise defined functions  

Section 1.3: Rate of Change and Behavior of Function.

Section 1.3.pdf Gegebra App One and Gegebra App Two

Learning objectives are

• The average rate of change for any function
• Forming difference quotient and simplification for polynomials and rational functions
• Behavior of the graph

Section 1.4: Composition of Functions- GroupWork 2

Section 1.4.pdf

Learning objectives are

• Review of all operations on functions
• Composition functions and their applications
• Finding the values of composition function using tables

Section 1.5: Transformation of functions.

Section 1.5.pdf
A Gegebra App

Learning objectives are

• Recognizing the transformations
• Finding the transformations of a graph
• Using Transformations to graph functions from a parent function

Section 1.6: Absolute Value Function.

Section 1.6.pdf
A Gegebra App

Learning objectives are

• Recognizing the absolute value function as a piecewise connected function
• Solving the equations with absolute values
• Solving inequalities with absolute values
• Graphs of absolute value functions

Section 1.7: Inverse Functions.

Section 1.7.pdf

Learning objectives are

• Definition and recognition of one to one functions
• Restriction of the domains
• Finding inverse using the rule of function
• Finding inverse using the graph of the function
• Applications

Quiz 1 Videos

Sections 2.1-2.2: Linear Functions and Their Graphs.

Sections 2.1-2.2.pdf
A Geogebra App

Learning objectives are

• Slope of a line
• Equation of a line
• Intersection of two lines
• Rate of Change of Linear Functions

Section 2.3: Modeling with Linear Functions.

Section 2.3.pdf
A Geogebra App

Learning objectives are

• Problems that can be modeled by Linear Functions
• Intersection of two lines determines which method is more efficient

Section 3.1: Complex Numbers.

Section 3.1.pdf

Learning objectives are

• The existence as they are roots of ploynomials
• Solutions to quadratic
• Addition and subtraction
• Multiplication
• Conjugate and division
• Forbidden operations
• Complex plane

Section 3.2: Quadratic Functions.

Section 3.2.pdf
Geogebra App One and Geogebra App Two

Learning objectives are

• Completing the squares
• Vertex
• Graph and behavior
• Optimization Models

Section 3.3: Power Functions.

Section 3.3.pdf
A Geogebra App

Learning objectives are

• Recognition of power and polynomial functions
• Graphs of power functions
• End behavior of polynomial functions
• Multiplicity of zeros of polynomial functions
• Modeling with polynomials

Section 3.4: Graphs of Polynomial Functions.

Section 3.4.pdf
A Geogebra App

Learning objectives are

• Graphing a polynomial
• More on end-behavior
• multiplicity of the roots
• Local maximum and minimum of polynomials
• Continuity of the graph of polynomials
• More on Modeling with polynomials

Section 3.5: Dividing Polynomials.

Section 3.5.pdf

Learning objectives are

• Various methods of finding and verifying roots
• Synthetic division
• Long division

Section 3.6: Zeros of Polynomial Functions.

Section 3.6.pdf A Geogebra App

Learning objectives are

• Formalizing Factor Theorem from last section
• Fundamental Theorem of Algebra
• Linear Factorization Theorem
• Linear and Quadratic Theorem
• Rational Roots Theorem
• Alternating Roots Theorem
• Finding zeros of a polynomial using all of the theorems

Section 3.7: Rational Functions.

Section 3.7.pdf A Geogebra App

Learning objectives are

• Asymptotes and end behavior of rational functions
• Simplifying rational expressions
• Solving rational equations
• Modeling rational equations

Section 3.8: Radical Functions And Inverses.

Section 3.8.pdf

Learning objectives are

• Domain restrictions
• Graph of inverse
• Solving Radical Equations

Group Work 4:

Group Work 4.pdf (Solution Will be Posted on Canvas Only.)

Section covered in this GroupWork are

• Section 3.1
• Section 3.2
• Section 3.3
• Section 3.4
• Section 3.5

Section 4.1: Exponential Functions.

Section 4.1.pdf
A Geogebra App

Learning objectives are

• Introduction to exponentials
• Euler number
• Continuous growth
• Interest
• Compounded interest

Section 4.2: Graph of Exponential Functions.

Section 4.2.pdf A Geogebra App

Learning objectives are

• Graphs of exponential functions
• Asymptotes
• Domain and range

Section 4.3: Logarithmic Functions.

Section 4.3.pdf

Learning objectives are

• Introduction to logarithm of different basis
• Asymptotes
• As an inverse function
• Domain and range
• Applications

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Section 4.4: Graph of Logarithmic Functions.

Section 4.4.pdf

Learning objectives are

• Graphing Logarithmic Functions
• Intercepts, Asymptotes and transformations

Section 4.5: Exponential and Logarithmic Properties.

Section 4.5.pdf

Learning objectives are

• Laws of Exponential
• Laws of Logarithm
• Simplification and expanding expressions using those laws.

Section 4.6: Exponential And Logarithmic Equations.

Section 4.6.pdf

Learning objectives are

• Solving equations which have logarithmic expressions
• Solving equations which have exponential terms

Section 4.7: Modeling with the Exponential and Logarithmic Functions.

Section 4.7.pdf

Learning objectives are

• Finding the growth and decay rates
• Half-life and doubling time
• Solving equation created in the models.

Section 5.1: Angles.

Section 5.1.pdf
Geogebra App One and Geogebra App Two

Learning objectives are

• Conversion of degrees to radian
• Coterminal angles
• Introduction to the unit circle
• Angular speed
• Sectors area and arc length

Section 5.2: Unit Circles: Sine And Cosine Functions.

Section 5.2.pdf
A Geogebra App

Learning objectives are

• Sine and Cosine
• Coterminal and reference angles

Section 5.3: The Other Trigonometric Functions.

Section 5.3.pdf

Learning objectives are

• Tangent and cotangent
• Trigonomtric identities relating the functions together

Section 5.4: Right Triangle Trigonometry.

Section 5.4.pdf
A Geogebra App

Learning objectives are

• Finding the trigonometric functions using a right triangles (Reference Triangles)
• Modeling with trigonometric functions

Section 6.1: Graphs of Sine and Cosine.

Section 6.1.pdf
A Geogebra App

Learning objectives are

• Graph of the functions
• Period of Sine and Cosine
• Magnitude and phase
• Simple harmonic motion

Section 6.2: Graphs of Other Trigonometric Functions.

Section 6.2.pdf


Learning objectives are

• Asymptotes
• Domain and range

Section 6.3: Inverse of Trigonometric Functions.

Section 6.3.pdf
A Geogebra App

Learning objectives are

• Graphs of inverse functions
• Restricting the domain
• Composition of trigonometric functions and inverses
• Using right triangle to find the inverse values

Section 7.1: Trigonometric Identities And Equations.

Section 7.1.pdf


Learning objectives are

• Learning how to infer the simple Trigonometric identities
• Recognizing the difference between equations and the identities
• Proving and verifying complex trigonometric identities

Section 7.2: Sum and Difference Identities.

Section 7.2.pdf
A Geogebra App

Learning objectives are

• Using the sum identities to verify the difference identities
• Using the sum and difference identities to find the exact trigonometric values of new angles
• Using the sum identities to prove other identities

Section 7.3: Double_angle, Half_angle, and Reduction Formula.

ection 7.3.pdf


Learning objectives are

• Derivation of all of these formulas from the sum identities
• Using the formulas to find exact values for angles
• Using the formulas to solve trigonometric equations
• Performing the reduction

Section 7.4: Sum-to-product and Product-to-sum Formula. and

Section 7.4.pdf


Learning objectives are

• Verifying the formulas
• Using the formulas to solve equations

Section 7.5: Solving Trigonometric Equations.

Section 7.5.pdf


Learning objectives are

• Finding values of trigonometric functions in an equation using factoring, substitution, quadratic equations and various identities
• Solving for the inverse functions, using known values or arc functions, in one period of inside angle
• Solving in the entire domain by adding multiple of periods.

Section 7.6: Modeling with Trigonometric Functions.

Section 7.6.pdf
A Geogebra App

Learning objectives are

• Emphasis on finding the period, phase shift, midline and amplitude
• Using the information to find A a sine or cosine to model
• Using trigonometric functions to model
• Combining linear functions and Pythagorean theorem to model distance in case of constant speed.

Section 8.1: Non-right Triangles, Law of Sines.

Section 8.1.pdf
A Geogebra App

Learning objectives are

• A brief verification of the law
• How to solve for all sides and angles in case of SAS, ASA, SSA and AAS
• Understanding that SSA may have one or two congruence triangles if any
• Modeling with law of sines

Section 8.2: Non-right Triangles, Law of Cosines.

Section 8.2.pdf

Learning objectives are

• A brief Verification of the law
• How to solve for all angles in case of SSS
• Modeling with law of cosines

Section 8.3: Polar Coordinates.

Section 8.3.pdf
A Geogebra App

Learning objectives are

• Conversion from Cartesian to Polar
• Conversion from Polar to Cartesian
• How to interpret if the radius is negative

Section 8.4: Polar Coordinates: Graphs.

Section 8.4.pdf
Geogebra App One, Geogebra App Two and Geogebra App Three

Learning objectives are

• Symmetries of the graph
• Graphing Circles, Cardioid, Limacons, Lemniscates and Archimedes' Spiral

Section 8.5: Polar Form of Complex Numbers.

Section 8.5.pdf (Solution)

Learning objectives are

• How to find the polar form
• How to use the polar form to do multiplication/division and raising to powers

Section 8.6 and 8.7: Parametric Equations and Graphs.

Sections 8.6-8.7.pdf
Geogebra App One, Geogebra App Two and Geogebra App Three

Learning objectives are

• Parameterizing Cartesian equations
• Converting parametrized curves to Cartesian equations
• Recognition of popular parametrization of line, circle and ellipse
• Law of gravity and parametrization of a projectile

Section 9.1 and 9.2: System Of Linear Equations: Two Variables

Section 9.1-9.2.pdf

Learning objectives are

• Geometric interpretation of two and three variables
• How to solve the systems using elimination method
• Word problems involving the systems
• Breaking even points for linear systems of cost and revenue

Section 9.3: Systems of Non-linear Equations and Inequalities.

Section 9.3.pdf
A Geogebra App

Learning objectives are

• Systems with linear and non-linear equations
• Using substitution and elimination
• Geometry of the solution
• The region between two curves

Section 9.5: Matrices and Matrix Operations.

Section 9.5.pdf
A Geogebra App

Learning objectives are

• Definition and dimensions
• Sum, difference and product of matrices
• Identity of sum and product

Section 9.6: Solving Systems with Gaussian Elimination.

Section 9.6.pdf
A Geogebra App

Learning objectives are

• Augmented matrix and how it is related to a system
• Row echelon forms
• Using row echelon form to rewrite a row equivalent system

Sections 10.1: The Ellipse.

Section 10.1.pdf
Geogebra App One and Geogebra App Two

Learning objectives are

• Equation of ellipse centered at origin with major axis horizontal or vertical
• Writing equations of ellipses in standard forms
• Finding equation of a vertical or horizontal ellipse that is not centered at origin
• Finding the intercepts and foci of vertical and horizontal ellipses

Sections 10.2: The Hyperbola.

Section 10.2.pdf
A Geogebra App

Learning objectives are

• Finding equations of vertical and horizontal hyperbolas centered at any point
• Foci and asymptotes of vertical and horizontal hyperbolas
• We don't discuss other hyperbolas in this section but we discussed the ones with vertical and horizontal asymptotes in Chapter 3



Videos

Sections 10.3: The Parabolas

Section 10.3.pdf
Geogebra App One and Geogebra App Two

Learning objectives are

• Vertical and horizontal parabolas
• How to find the foci and directrix using the equation
• The concave mirror