Functions and Transformations

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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

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 functions

Linear Equations

Sketching linear functions

Find the equation of a given line

Parallel and perpendicular lines

Simultaneous equations

Quadratics

The discriminant

Linear transformation

Transformation of quadratics

The Absolute function

Hybrid (piecewise) functions

Inverse Functions

Graphs of exponential and logarithmic functions

Composite functions

Graphs of sine and cosine trig functions

Phase shift

Changing amplitude and period of sine and cosine functions

Vertical shift and putting it all the transformations together

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How to get the most out of this course

This 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

Who this course is for:

• 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.

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