Teach on Udemy

Turn what you know into an opportunity and reach millions around the world.

Learn More

Your cart is empty.

Keep shopping

Ace Advanced Functions/Precalculus in 6 Hr (Complete Course)

Name: Ace Advanced Functions/Precalculus in 6 Hr (Complete Course)
Rating: 4.8 (11 reviews)

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

Created byGina Chou

Last updated 1/2025

English

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)
Factor a polynomial function and sketch the function without a graphical calculator
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

Course content

7 sections • 53 lectures • 5h 47m total length

Overview2:17
Welcome and How It Works2:32
Tips to Maximize Your Learning0:30

Downloadable Notes0:03
What is a Function?6:25
Explore the definition of a function as a mapping from input to a single output, using x squared and the domain and range to show independent and dependent variables.
Domain and Range of a Function4:33
Vertical and Horizontal Line Tests8:26
Properties of Graphs13:45
Average Rate of Change4:33
Review: Factoring Techniques11:48
Examples: Domain and Range19:02
Example: Function Behavior5:53
This example shows behavior with roots at -2, 1, and 3; a horizontal asymptote at -2; a local min at -1 and max at 2; inflection near 2.5 and 2.4.
Example: Average Rate of Change4:16
Example: Piecewise Function3:32
Example: Multivariable Function5:18
Functions and Graphs

Downloadable Notes0:03
Combinations of Functions10:14
Transformations8:02
Even and Odd Functions6:05
Determine if a function is even or odd by evaluating f(-x); even functions are preserved under y-axis reflection, odd functions under 180-degree rotation, illustrated by 2x^2, 2x^3, and 2x^2+x.
Inverse Functions5:26
Properties of Inverses6:56
Example: Combinations of Functions10:48
Example: Transformations9:05
Example: Even or Odd Functions4:08
Identify whether a function is even, odd, or neither by computing f(-x) and comparing to f(x) or -f(x); examples include 1/x (odd), x^4 - x^2 (even), and (2+x)/(1+x^2) (neither).
Examples: Inverse Functions6:49
Operations, Transformations, and Inverses

Downloadable Notes0:03
Algebraic Functions3:01
Power Functions4:00
Polynomial Functions12:31
Study polynomial functions as finite sums of power terms; identify coefficients, leading coefficient, and leading term; analyze end behavior and turning points to infer roots and graph shape.
Rational Functions8:31
Absolute Value Functions5:14
Example: Domains of Power Functions5:12
Example: Graph of a Polynomial5:01
Example: Sketch a Rational Function7:55
Example: Absolute Value Function5:36
Algebraic Functions

Downloadable Notes0:03
Transcendental Functions1:07
Exponential Functions8:10
Explore exponential functions defined as a times b^x. Base b is positive and not 1; include natural base e, growth and decay, and the zero horizontal asymptote.
Logarithmic Functions8:08
Explore the logarithmic function as the inverse of exponential functions, with base B and input X, and learn key log rules, change-of-base, and the natural log special case.
Unit Circle7:40
Trigonometric Functions16:19
Inverse Trigonometric Functions6:27
Examples: Solve Transcendental Functions10:15
Solve transcendental functions by hand using log properties and exponential transformations, and apply unit circle techniques to cosine at pi over six and inverse sine and inverse secant.
Example: Graphs of Transcendental Functions9:43
Example: Inverse of Transcendental Functions2:34
Transcendental Functions

Requirements

Familiarity with algebra
Some basic knowledge with the cartesian coordinates

Description

HOW THIS COURSE WORK:

This course, Ace Advanced Functions/Precalculus in 6 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 Graphs
Operations, Transformations, and Inverses
Algebraic Functions
Factorization of Polynomials (NEWLY ADDED SECTION)
Transcendental Functions

CONTENT 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 success
Lifetime access to Ace Precalculus in 6 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: Five 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 :)

Who this course is for:

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

Ace Advanced Functions/Precalculus in 6 Hr (Complete Course)

What you'll learn

Explore related topics

Course content

Introduction3 lectures • 5min

Functions and Graphs12 lectures • 1hr 28min

Operations, Transformations, and Inverses10 lectures • 1hr 8min

Algebraic Functions10 lectures • 57min

Factorization of Polynomials (NEWLY ADDED SECTION)6 lectures • 58min

Transcendental Functions10 lectures • 1hr 10min

Conclusion2 lectures • 1min

Requirements

Description

Who this course is for: