Functions And Transformations

Learn functions such as linear, quadratic, absolute, hybrid, inverse, composite, trig and master their transformations.

What you'll learn

Learn about the fundamental concept of a function

Sketch linear functions including vertical and horizontal lines.

Learn to find the equation of a line from a graph and find the equation of a line from two coordinates.

Calculate the equations of parallel and perpendicular lines.

Solve linear equations simultaneously using substitution and elimination .

Identify and sketch quadratic functions.

Calculate and interpret the discriminant.

Perform transformations of linear, Quadratic and Trigonometric functions.

Understand the concept, graphs and transformations of absolute functions.

Sketch hybrid/piecewise functions and state their domain and range.

Inverse functions.

Graph exponential and logarithmic functions.

Composite functions.

Requirements

If you have basic number and algebra skills you will learn everything you need to know.

Description

The aim of this course is to provide you with an introduction to and a solid basis for further study in mathematics in the fields of science, mathematics, business, economics and engineering. An understanding of functions, transformations and their applications will give you the skills needed in modeling and lay a foundation for more advanced math and science course. Learn from a mathematician and master educator in this streamlined course designed to teach you exactly what you need to know. Use the companion student booklet to practice what you have learned as well as checking your responses with the provided worked solutions.This course will cover Introduction to functionsLinear EquationsSketching linear functions Find the equation of a given lineParallel and perpendicular linesSimultaneous equationsQuadraticsThe discriminantLinear transformationTransformation of quadraticsThe Absolute functionHybrid (piecewise) functionsInverse FunctionsGraphs of exponential and logarithmic functionsComposite functionsGraphs of sine and cosine trig functionsPhase shiftChanging amplitude and period of sine and cosine functionsVertical shift and putting it all the transformations together How to get the most out of this courseThis course is broken up into small individual sections designed to help you learn exactly what you need to know, maximising your time. View the tutorial video and follow along. Pause and take notes as needed. After each of the tutorial videos you will find a ‘check of understanding’ which consists of 5 questions that relate to the material covered in the video/s. Complete the questions and check your Answers with the worked solutions so you can see how you are progressing.

Overview

Section 1: Introduction

Lecture 1 Introduction

Section 2: Linear Functions

Lecture 2 Introduction to functions

Lecture 3 Linear Equations

Lecture 4 Sketching linear functions Video 1

Lecture 5 Sketching linear functions Video 2

Lecture 6 Find the equation of a given line

Lecture 7 Parallel and perpendicular lines

Lecture 8 Simultaneous equations

Lecture 9 Quadratics

Lecture 10 The discriminant

Lecture 11 Linear transformation

Lecture 12 Transformation of quadratics

Lecture 13 The Absolute function

Lecture 14 Hybrid (piecewise) functions

Lecture 15 Inverse Functions

Lecture 16 Graphs of exponential and logarithmic functions

Lecture 17 Composite functions

Lecture 18 Graphs of sine and cosine trig functions

Lecture 19 Phase shift

Lecture 20 Changing amplitude and period of sine and cosine functions

Lecture 21 Vertical shift and putting it all the transformations together Video 1

Lecture 22 Vertical shift and putting it all the transformations together Video 2

This course is for anyone who wants to master the basic concepts of Functions and Transformations, in order to build a strong base in mathematics.