Ace Precalculus In 5 Hours (The Complete Course)

Learn the connections between numeric, graphical, and algebraic representations of relations and functions

What you'll learn

Identify whether a rule is a function

Find the domain and range of a function (algebraic and transcendental functions)

Identify whether a graph is a function by using the vertical line test

Identify whether a graph is a one-to-one function by using the horizontal line test

Understand and identify properties of a graph (x- and y-intercepts, roots, local extrema, concavity, increasing/decreasing, inflection point, and more)

Calculate the average rate of change of a function over an interval

Find the domain of a combination of functions

Understand transformations of functions (translations, expansion/compression, and reflection)

Sketch a function using transformations of functions

Determine whether a function is an even or odd function, or neither

Find the inverse of a function algebraically and graphically

Learn the algebraic and graphical properties of algebraic functions (power, polynomial, and rational functions)

Understand and evaluate absolute value functions

Learn the algebraic and graphical properties of transcendental functions (exponential, logarithmic, trigonometric, and inverse trigonometric functions)

Evaluate transcendental functions without using calculator

Convert angles from degrees to radians and from radians to degrees

Find the exact values of trigonometric and inverse trigonometric functions using the unit circle

Requirements

Familiar with algebra

Some basic knowledge with the cartesian coordinates

Description

HOW THIS COURSE WORK:This course, Ace Precalculus in 5 Hours (The Complete Course), is intended to introduce the student to advanced functions and prepare the student to take calculus courses in the future. The course includes videos, notes from whiteboard during lectures, and practice problems (with solutions!). I also show every single step in examples and proofs. The course is organized into the following topics:Functions and GraphsOperations, Transformations, and InversesAlgebraic FunctionsTranscendental FunctionsCONTENT YOU WILL GET INSIDE EACH SECTION:Videos: I start each topic by introducing and explaining the concept. I share all my solving-problem techniques using examples. I show a variety of math issue you may encounter in class and make sure you can solve any problem by yourself.Notes: In each section, you will find my notes as downloadable resource that I wrote during lectures. So you can review the notes even when you don't have internet access (but I encourage you to take your own notes while taking the course!).Assignments: After you watch me doing some examples, now it's your turn to solve the problems! Be honest and do the practice problems before you check the solutions! If you pass, great! If not, you can review the videos and notes again before moving on to the next section.THINGS THAT ARE INCLUDED IN THE COURSE:An instructor who truly cares about your successLifetime access to Ace Precalculus in 5 Hours (The Complete Course)HIGHLIGHTS:#1: Downloadable lectures so you can watch the videos whenever and wherever you are.#2: Downloadable lecture notes so you can review the lectures without having a device to watch/listen.#3: Four problem sets at the end of each section (with solutions!) for you to do more practice.#4: Step-by-step guide to help you solve problems.See you inside the course!- Gina :)

Overview

Section 1: Introduction

Lecture 1 Overview

Lecture 2 Welcome and How It Works

Lecture 3 Tips to Maximize Your Learning

Section 2: Functions and Graphs

Lecture 4 Downloadable Notes

Lecture 5 What is a Function?

Lecture 6 Domain and Range of a Function

Lecture 7 Vertical and Horizontal Line Tests

Lecture 8 Properties of Graphs

Lecture 9 Average Rate of Change

Lecture 10 Review: Factoring Techniques

Lecture 11 Examples: Domain and Range

Lecture 12 Example: Function Behavior

Lecture 13 Example: Average Rate of Change

Lecture 14 Example: Piecewise Function

Lecture 15 Example: Multivariable Function

Section 3: Operations, Transformations, and Inverses

Lecture 16 Downloadable Notes

Lecture 17 Combinations of Functions

Lecture 18 Transformations

Lecture 19 Even and Odd Functions

Lecture 20 Inverse Functions

Lecture 21 Properties of Inverses

Lecture 22 Example: Combinations of Functions

Lecture 23 Example: Transformations

Lecture 24 Example: Even or Odd Functions

Lecture 25 Examples: Inverse Functions

Section 4: Algebraic Functions

Lecture 26 Downloadable Notes

Lecture 27 Algebraic Functions

Lecture 28 Power Functions

Lecture 29 Polynomial Functions

Lecture 30 Rational Functions

Lecture 31 Absolute Value Functions

Lecture 32 Example: Domains of Power Functions

Lecture 33 Example: Graph of a Polynomial

Lecture 34 Example: Sketch a Rational Function

Lecture 35 Example: Absolute Value Function

Section 5: Transcendental Functions

Lecture 36 Downloadable Notes

Lecture 37 Transcendental Functions

Lecture 38 Exponential Functions

Lecture 39 Logarithmic Functions

Lecture 40 Unit Circle

Lecture 41 Trigonometric Functions

Lecture 42 Inverse Trigonometric Functions

Lecture 43 Examples: Solve Transcendental Functions

Lecture 44 Example: Graphs of Transcendental Functions

Lecture 45 Example: Inverse of Transcendental Functions

Section 6: Conclusion

Lecture 46 Thank You & Good Luck & Next Step

Lecture 47 BONUS: Let's Keep Learning!

Students about to start precalculus or calculus who are looking to get ahead,Current precalculus students who are looking for extra help on functions and graphs,Homeschool parents looking for extra support with precalculus,Homeschool parents whose child is interested in taking calculus courses in university,Anyone who is familiar with algebra and is interested in more advanced math and calculus