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Different notations are used in different areas of life depending on the audience. This lesson reviews the inequality notation and word descriptions. Then we explore the new interval notation and how to use it.

Review of Practice

Properties of Graphs

Review Practice

Properties determined from the equations.

Review Practice

Explore the relationship between the function and infinity.

Review Practice

This lessons introduces the following nine parent functions that are studied in greater detail later in the course: linear, absolute value, quadratic, square root, cubic, cube root, rational, exponential, and log. We learn how to recognize the type of parent function from a description, an equation, or a graph. Each of the notes videos are about 5 minutes long. The examples and review of practice problems videos are over 10 minutes each. Watch all of the videos first and take the notes. Then work the practice problems for all parts are in this lesson.

Introduction to the quadratic parent function.

Introduction to square root parent functions

Introduction to absolute value parent functions

Introduction to cubic parent functions

Introduction to cube root parent functions

Introduction to rational parent functions

Introduction to exponential parent functions

Introduction to Log parent functions

Examples based on notes from all parts

Practice problems using knowledge from all parts. Documents are in Part 1 of lesson.

How changes in the parent function affect the graph and other properties. Notes & practice include work for parts 1 & 2.

Review Practice

How changes in the equation affect the graph and other properties. All notes and practice are attached to part 1.

Review Practice

Review of the relationship for collected data. and determining the type of function.

Review Practice

Review of the relationship for collected data. and determining the type of function.

Review practice

Finding the function that best fits the data to predict outcomes. TI-84 required.

Review Practice

Short research activity applying modeling of data with real research.

For the few absolutes in life we write equations.

Review Practice

Review Practice

In life things are not always equal.

Review Practice

Combining the absolute value function and inequalities give real world application.

Review Practice

Review word problem practice

Short project designed to help students apply this knowledge to the real world.

Review how to graph linear equations and use to solve systems.

Review Practice

Brief project to apply knowledge to real world scenario.

Review of graphing linear inequalities and using them to solve systems.

Word problems = applications of the math.

Review practice

Review of solving 2x2 systems from algebra 1.

Using the substitution method to solve 3x3 systems.

Review practice

Review of solving 2x2 systems from algebra 1.

Using the Elimination method to solve 3x3 systems.

Review Practice

This is not about the movies! A matrix is another method for solving systems of equations.

Review Practice

In order to use a matrix to solve, we have to find the determinant and the inverse of a matrix.

Review Practice

Finally the Solving! You need a TI-84 or TI-85 for this lesson. I will show how to solve by hand and by calculator.

Review Practice

Food for thought activity from the bottom of the notes.

Review of Greatest Common Factor

Review Practice

factoring quadratics with a lead coefficient equal to one.

Review Practice

Factoring quadratics with a lead coefficient not equal to one.

Review Practice

Factoring polynomials with a degree greater than two.

Review Practice

There is a shortcut for perfect cubes! Here is the trick...

Review Practice

Explore finding the properties of a quadratic from graphs and real-world applications

Review Practice

Identify and use complex numbers and root

Review Practice

Solve quadratic equations using the quadratic formula.

Review Practice

Solve quadratic equations using the complete the square method.

Review Practice

Solve quadratic inequalities using a table or a graph.

Review Practice

Change from one form of the quadratic to another to find key information.

Review Practice

Write a quadratic given different pieces of information.

Review Practice

Use the information from the Quadratic Lessons to fly to the moon...or at least throw a football on the moon.

Graphing square root and cube root equations and inequalities.

Review Practice

Add and subtract square roots and cube roots

Review Practice

Multiply, divide, and simplify square roots and cube roots

Review Practice

Review Practice

Solve square root and cube root equations

Review Practice

Solve and graph radical inequalities

Review Practice

Square root functions in the world

Review Practice

Application Project

Add and Subtract polynomial expressions

Review Practice

Multiplying polynomials of all shapes and sizes

Review practice

A shortcut method for multiplying binomials to a power.

Review Practice

First method to dividing polynomials.

Review Practice

Shortcut division process and theorems that can be used instead of long division.

Review Practice

Use all of the polynomial lessons, including end behaviors and graphs from the beginning.

Direct, inverse and joint variation and how it describes real world relationships.

Review Practice

Add & subtract rational expressions in order to simplify

Review Practice

Simplify rational expressions

Review Practice

Simplify & multiply rational expressions

Review Practice

Divide & simplify rational expressions

Review Practice

find the solution for the rational equations

Review Practice

Identify key information and graph the parent function form of the rational equation.

Review Pratice

Identify key information and graph the standard form of the rational equation.

Review Practice

How are rational functions used in the real world?

Review Practice

Optional application project

How are exponents and radicals are the same thing?

Review Practice

What to do with exponents when multiplying?

Review Practice

What to do with exponents when dividing?

Review Practice

Review of zero exponents. What to do with negative exponents?

Review Practice

How to transform the graphs of exponential functions using points.

Review Practice

How can I make more money?

Review Practice

Exponential growth and decay in life.

Review Practice

Using data to find answers and the exponential equations.

Review Practice

Investment project and medicine vs. bacteria project.

Introduction to logarithm functions, converting logs to exponents, and solving very simple logs.

Review Practice

Expand and solve logs

Review Practice

Condensing logs and solving

Review Practice

How to change the base of a log to use the preprogrammed calculator buttons.

Review Practice

How to solve 3 different types of logarithm equations.

Review Practice

How to accurately graph log equations and inequalities.

Review Practice

Applications of Log in real world scenarios

Review Practice

Research and apply what you have learned about logs.

Modeling Log equations and inequalities

Review Practice

A new notation for combining functions and simplifying functions.

Review Practice

Inverse is like opposite. Find the opposite of this function.

Review Practice

Functions with domain restrictions and different pieces on the graph.

Review Practice

The fall final exam includes the following units: Functions, Parent Functions, Modeling, Absolute Value, Systems, Matrices, Factoring, and Quadratics.

The spring final exam includes the following units: Radicals, Polynomials, Rationals, Exponents, Logs, and Non-parent functions.

**Course Description:**

In this course I guide the students step by step through applying the fundamental skills of mathematics to such topics as functions, equations and inequalities, radicals and rational expressions, logarithmic and exponential relationships, quadratic and polynomial equations, and matrices. The student will be introduced to key concepts and theories that provide a foundation for further study in mathematics (College Algebra, PreCalculus, Calculus, and beyond) and increases students’ mathematic literacy, problem solving, and critical thinking skills. Real world scenarios will be used to introduce and expand upon the topics discussed in each unit. Use of graphing calculators will be incorporated into many of the lessons.

**Course Goals:**

Upon completion of this course student will know how to recognize, graph, perform operations (add, subtract, multiply, divide), solve, and apply each parent function. Additionally students will be prepared for PreCalculus (or Geometry which is also a prerequisite for PreCal).

**Target Audience:**

This course is intended for students that have completed Algebra 1 and Math grades 6-8. Geometry is optional, but should be completed before taking Precalculus. Students will be using a TI-84 or TI-85 calculator as part of the lessons.

**Course Includes:**

52.6 Hours of Video (lessons and working of practice problems)

14 Units

83 Video Lessons

83 Exercise Review Videos (where I go over each exercise problem step by step)

73 Outlined notes, Practice Problems and Paper Quizzes (each lesson)

10 Project Lessons (no quizzes)

82 Short Tests (paper & electronic for each lesson)

82 Test Answer Keys (for parents)

2 Paper Final Exams

Parent resources for each lesson include pdf keys of notes, practice problems, paper quizzes and electronic quiz keys.

**Working Sequence:**

Step 1) Watch the explanatory video-lesson.

Step 2) Download the practice worksheets (Documents Section) and work on the activities.

Step 3) Watch the Exercise Review Video where I review each problem step-by-step.

Step 4) Take the online test for the lesson. The system will auto-correct. Answer key is provided under the Resources Section (only for parents)

Step 5) Once we finish the unit, we move on to the next unit. Be sure you understood the content and you worked on the activities before moving to another unit.

You can repeat steps 2 and 3 as many times as you like until you gain mastery of the topic. Each topic should take you 2 to 3 days on average to complete.

**Course Topics:**

Function Properties

Parent Functions

Modeling Fucntions

Absolute Value Functions

Systems of Functions

Matrices

Factoring

Quadratic Functions

Radical Functions

Polynomial Functions

Rational Functions

Exponential Functions

Log Functions

Non-Parent Functions

- Teacher: Shirly
- Areas of expertise: Aerospace Engineer: Algebra 1, 2, 3 and PreCalculus
- Education: Bachelor of Science from Texas A&M University
- Interests: Art, crafts, music, sewing, painting, cooking, and scrapbooking
- Skills: teaching, organizing, and innovation
- Associations: LDS
- Issues I care about: Having a high moral character.

My life is a journey. I enjoy the steps I make and see the world around me a little differently each time I learn something new. I spent 10 years in the Aerospace industry and worked on the International Space Station and the Apache helicopter programs. I have learned many things and want to share them with you.

Keys for Notes, Practice, and Quiz

Long & Synthetic Division

Parent function & standard form keys