Introduction to Precalculus: Functions and Graphs

person icon Gina Chou

Introduction to Precalculus: Functions and Graphs

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

updated on icon Updated on Nov, 2023

language icon Language - English

person icon Gina Chou

architecture icon Math,Calculus,Teaching & Academics

Lectures -18

Resources -4

Duration -1 hours


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Course Description


This course, Introduction to Precalculus: Functions and Graphs, includes the first chapter of a precalculus course, including video, 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:

  • Definition of a Function

  • Domain and Range of a Function

  • Vertical and Horizontal Line Test

  • Properties of Graphs

  • Average Rate of Change

  • Piecewise Function

  • Multivariable Function


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.


  • An instructor who truly cares about your success

  • Lifetime access to Introduction to Precalculus: Functions and Graphs


#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: One problem set at the end of the course (with solutions!) for you to do more practice.

#4: Step-by-step guide to help you solve problems.

See you inside the course!

- Gina :)


What will you learn in this course:

  • Identify whether a rule is a function
  • Find the domain and range of a function
  • 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


What are the prerequisites for this course?

  • Familiarity with algebra
  • Some basic knowledge with the cartesian coordinates
Introduction to Precalculus: Functions and Graphs


Check out the detailed breakdown of what’s inside the course

3 Lectures
  • play icon Course Outline
  • play icon Welcome and How It Works
  • play icon Tips to Maximize Your Learning
Functions and Graphs
13 Lectures
2 Lectures

Instructor Details

Gina Chou

Gina Chou

Physics PhD candidate

While I was in undergrad, I was always excited to take exams because I was always well prepared and I felt accomplished after finishing each exam. I know that it is not the case for most of the students. So here, I will share my knowledge and help you to make your university life easier! :D

More about my background

I received my BSc in Atmospheric Science and Physics with a minor in Mathematics from the McGill University in 2018 and my MSc in Physics at the University of Toronto in 2019. I am currently a Ph.D. candidate in the Physics Department and I am interested in the impact of wind observation on the global predictability, Arctic climate, and weather processes.

Since my second year of undergraduate studies, I have had extensive tutoring experiences, teaching at Liberty Tutoring, as well as high school and university students through SUS Peer Tutoring and Saturday Programs. Additionally, I have been/currently am a TA for math and physics undergraduate and graduate courses.

I hope to see you in class!

- Gina C.

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