Download presentation

Presentation is loading. Please wait.

Published byVanessa Pratt Modified over 4 years ago

1
A transformation is an algebraic change to a function which affects the shape or position of the graph. Introduction to Transformations What is the difference between and ? y = f ( x) + ay = f ( x) + ay = f ( x + a)y = f ( x + a) x f (x)f (x) + a+ a y x f (x)f (x) + a+ a y y = f ( x) + ay = f ( x) + a y = f ( x + a)y = f ( x + a) Making a change after the function will affect only the Making a change before the function will affect only the y x -coordinate. Higher Maths 1 2 2 Transformations1

2
Any change to the position of a graph is called a translation. Translation y = f ( x) + ay = f ( x) + a Slides the graph of vertically. f ( x)f ( x) a f ( x) + af ( x) + a f ( x)f ( x) y = f ( x + a)y = f ( x + a) Slides the graph of horizontally. f ( x)f ( x) a f ( x + a)f ( x + a) f ( x)f ( x) up down + a+ a – a– a left right + a+ a – a– a Higher Maths 1 2 2 Transformations2

3
If the positive and negative coordinates of a graph are inverted, the graph will be reflected across either the x or y -axis. Reflection y = - f ( x ) Reflects the graph of f ( x ) vertically across the x -axis. - f ( x)- f ( x) f ( x)f ( x) y = f ( - x ) Reflects the graph of f ( x ) horizontally across the y -axis. f (- x)f (- x) f ( x)f ( x) Higher Maths 1 2 2 Transformations3

4
If every coordinate is multiplied by the same value, the overall shape of the graph will be distorted. Distortion y = a f ( x)y = a f ( x) f ( x)f ( x) a f ( x)a f ( x) Changes the vertical size of the graph of f ( x ). a > 1 stretch a < 1 compress y = f (a x)y = f (a x) f ( x)f ( x) Changes the horizontal size of the graph of f ( x ). a < 1 stretch a > 1 compress f (a x)f (a x) Higher Maths 1 2 2 Transformations4

5
The diagram below shows the graph of. Sketch. Sketching Composite Transformations Higher Maths 1 2 2 Transformations5 Example y = - 2 f ( x + 3 ) y = f ( x ) y = f ( x + 3 ) (3,0) ( - 2, - 2) ( - 5,4) (0, - 2) Remember to label all relevant coordinates. Important y = - 2 f ( x + 3 )

Similar presentations

OK

Pre-Cal Chapter 1 Functions and Graphs Section 1.5 Graphical Transformations.

Pre-Cal Chapter 1 Functions and Graphs Section 1.5 Graphical Transformations.

© 2018 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google