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Introduction to Precalculus: Functions and Graphs

person icon Gina Chou

4.6

Introduction to Precalculus: Functions and Graphs

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

updated on icon Updated on Jun, 2025

language icon Language - English

person icon Gina Chou

category icon Teaching and Academics ,Math,

Lectures -18

Resources -4

Duration -1 hours

Lifetime Access

4.6

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Course Description

HOW THIS COURSE WORK:

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


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.


THINGS THAT ARE INCLUDED IN THE COURSE:

  • An instructor who truly cares about your success

  • Lifetime access to Introduction to Precalculus: Functions and Graphs


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: 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 :)

Goals

  • 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

Prerequisites

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

Curriculum

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

Introduction

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
Tutorialspoint

Conclusion

2 Lectures
Tutorialspoint

Instructor Details

Gina Chou

Gina Chou

During my undergraduate years, I always looked forward to exams because I was well-prepared and found them rewarding. I know this isn’t the case for everyone, so I'm here to share my knowledge and help make your university journey a bit easier!

A bit about me:

I earned my BSc in Atmospheric Science and Physics, with a minor in Mathematics, from McGill University in 2018. I then completed my MSc in 2019 and my PhD in 2024, both in Physics at the University of Toronto. My research focuses on the impact of wind observations on global predictability, Arctic climate, and weather processes.

Since my second year of undergrad, I’ve gained extensive tutoring experience, working with students at Liberty Tutoring, supporting high school and university students through SUS Peer Tutoring and Saturday Programs, and working with private students both in person and online. I also served as a teaching assistant for math and physics courses at both the undergraduate and graduate levels from 2017 to 2024.

I look forward to seeing you in class!

Gina C.

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