2. Functions and Graphs

Determine Domains for Composite Functions

Combinations of Functions, Composite Functions

Ex 4:  Domain of a Composite Function

Combining functions by adding and subtracting

Expressing a function as a composition of two functions

Decomposing Functions - Composition of Functions

Domain of a Composition of Functions, Example 3 - Common Mistake

❖ Composition of Functions ❖

Finding Functions that Form a Particular Composite Function

Finding domain of composite functions

Finding the Domain of a Rational Function / Fraction with Variable in Denominator

Domain of a Composition of Functions, Example 2

Finding Domain of Functions Involving Radicals (Square Roots to be More Precise!) - Example 2

Rational Expressions and Domain

Algebra, Domain and Range

Domain of a Composition of Functions, Example 1

❖ Finding the Domain of a Function Algebraically (No graph!) ❖

Find the domain and range of a function

Learn How to Compose Two Rational Functions and Simplify

Express A Function As A Composition Of Two Functions

Manipulating Functions Algebraically and Evaluating Composite Functions

❖ Finding the Domain of a Function -  Made Easy! ❖

Functions: Adding and Subtracting

❖ Function Notation ❖

Combining functions by dividing

❖ How to Find the Domain of a Function - Numerous Examples ❖

Understand restrictions on functions in terms of domain and range

Learn the toughest concepts covered in Precalculus with step-by-step video tutorials and practice problems by world-class tutors 

Precalculus

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1. Fundamental Concepts of Algebra

3. Polynomial and Rational Functions

4. Exponential and Logarithmic Functions

5. Trigonometric Functions

6. Analytic Trigonometry

7. Additional Topics in Trigonometry

8. Systems of Equations and Inequalities

9. Matrices and Determinants

10. Conic Sections and Analytic Geometry

11. Sequences, Induction, and Probability

12. Introduction to Calculus

Verify Inverse Functions

Find the Inverse of a Function

Determine if a Function Has an Inverse Function (Using Horizontal Line)

Graph Inverse Function (use one-to-One Function graph)

Find the Inverse of a Function and Graph Both Functions 

Inverse Functions

Identify Intervals on Which a Function Increases, Decreases, or Is Constant

Use Graphs to Locate Relative Maxima or Minima

Test for Symmetry

Identifying Even or Odd Functions and Recognize Their Symmetries

Understand and Use Piecewise Functions

Find and Simplify a Function's Different Quotient

More on Functions and Their Graphs

Plotting Points in the Rectangular Coordinate System

Graphing an Equation Using the Point-Plotting Method

Understanding the Viewing Rectangle

Identifying Intercepts

Interpret Information Given by Graphs

Graphs and Graphing Utilities

Construct Functions from Formulas

Construct Functions from Verbal Descriptions

Modeling with Functions

Calculate a Line's Slope

Write the Point-Slope Form of the Equation of a Line

Write and Graph the Slope-Intercept Form of the Equation of a Line

Graph Horizontal and Vertical Lines

Recognize and Use the General Form of a Line's Equation

Use Intercepts to Graph the General Form of a Line's Equation

Model Data with Linear Functions and Make Predictions

Linear Functions and Slope

Find the Domain and Range of a Relation

Determine Whether a Relation is a Function

Determine Whether an Equation Represents a Function

Evaluate a Function

Graph Functions by Plotting Points

Use the Vertical Line Test to Identify Functions

Obtain Information About a Function From Its Graph

Identifying the Domain and Range of a Function From Its Graph

Identify Intercepts from a Function's Graph

Basics of Functions and Their Graphs

Find the Distance Between Two Points

Find the Midpoint of a Line Segment

 Standard Form of a Circle's Equation

Center and Radius of a Circle Whose Equation Is in Standard Form

Convert the General Form of a Circle's Equation to Standard Form

Distance and Midpoint Formulas, Circles

Recognizing Graphs of Common Functions

Use Vertical Shifts to Graph Functions

Use Horizontal Shifts to Graph Functions

Use Reflections to Graph Functions

Use Vertical Stretching and Shrinking to Graph Functions

Use Horizontal Stretching and Shrinking to Graph Functions

Graph Functions Involving a Sequence of Transformations

Transformations of Functions

Find the Domain of a Function

Combine Functions Using the Algebra of Function

Form Composite Functions

Write Functions as Compositions

Find Slopes and Equations of Parallel and Perpendicular Lines

Interpret Slope as Rate of Change

Find a Function's Average Rate of Change

More on Slope

General Chemistry

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Study the key concepts of Physics with descriptive videos, questions, and more

Physics

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General Biology

Jason

Financial Accounting

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Dive deep into Psychology with videos, practice problems, and more.

Psychology

Microeconomics

The first in a two-course sequence introduces the basic structure and functions of the human body

Anatomy & Physiology

College Algebra covers algebraic topics and skills necessary to succeed in college-level math

College Algebra

Organic Chemistry

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Genetics

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GOB Chemistry

Microbiology

Cell Biology

Analytical Chemistry

Study topics incliding trogonometric functions, identities and equations, solutions of triangles, complex numbers, and other topics as time permits

Trigonometry

Learn the toughest concepts covered in Precalculus with step-by-step video tutorials and practice problems by world-class tutors

Biochemistry

Macroeconomics

Chemistry

Biology

Math

Business

Social Sciences

Michelle Barry Franco

Building Great Presentations

Eric Zackrison, PhD

Critical Thinking And Problem Solving

Sam Bennett

Embracing Times Of Uncertainty

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Emotional Intelligence Basics

Eugene Choi, PharmD

Enhancing Your Critical Thinking Skills

Jason Richardson, PsyD

Habits To Win Every Day

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Having Powerful Advanced Conversations

Don Gilman, EdD

How To Influence & Persuade

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Leadership Skills For Rising Stars

Listening To Lead

Michael Shermer, PhD

Making Decisions Under Uncertainty

Lynne Hurdle

Mistakes To Avoid When Resolving Conflict

Michael Veltri

Overcoming Decision Making Traps

Mike Vardy

Prioritizing Effectively

Secrets Of Effective Prioritization

Strategies To Build Up Your Creativity

Tools For Decision Making

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Unleash And Advance Your Creativity

Winning Collaboration: How To Work More Effectively With Different Personalities