KS5 Grade 11 - FUNCTIONS
Lesson 3...TRANSFORMING FUNCTIONS
![Picture](/uploads/1/3/3/4/13343229/2148581.jpg)
There are 3 different types of transformations:
TRANSLATIONS [can be represented using a column vector]
f(x) + k results in a vertical translation; up (k > 0) or down (k < 0)
f(x + k) results in a horizontal translation; left (k > 0) or right (k < 0)
REFLECTIONS
- f(x) results in a reflection of f(x) in the x-axis
f(- x) results in a reflection of f(x) in the y-axis
STRETCHES
f(q x) results in a stretch or compression in the horizontal direction of scale factor 1/q
p f(x) results in a stretch or compression in the vertical direction of scale factor p
TASK 1 - Textbook Pg21 Investigation
TASK 2 - Textbook Pg24 Ex 1I Q1
HOMEWORK - Textbook Pg24 Ex 1I Q2 - 5
TRANSLATIONS [can be represented using a column vector]
f(x) + k results in a vertical translation; up (k > 0) or down (k < 0)
f(x + k) results in a horizontal translation; left (k > 0) or right (k < 0)
REFLECTIONS
- f(x) results in a reflection of f(x) in the x-axis
f(- x) results in a reflection of f(x) in the y-axis
STRETCHES
f(q x) results in a stretch or compression in the horizontal direction of scale factor 1/q
p f(x) results in a stretch or compression in the vertical direction of scale factor p
TASK 1 - Textbook Pg21 Investigation
TASK 2 - Textbook Pg24 Ex 1I Q1
HOMEWORK - Textbook Pg24 Ex 1I Q2 - 5
Lesson 2...FUNCTION PROBLEMS
![Picture](/uploads/1/3/3/4/13343229/2713485.jpg)
Notation
Eg. x is less than 5, or greater than or equal to 6
Interval notation (-∞, 5) U [6, +∞)
Set builder notation {x : x < 5, x ≥ 6}
Evaluating functions
Eg. Find f(2) when f(x) = 4x - 3
f(2) = 4(2) - 3 = 5
A COMPOSITE FUNCTION is a combination of two or more functions
Eg. If f(x) = 3x - 7 and g(x) = 2x find (f o g)(x)
(f o g)(x) = 3(2x) - 7 = 6x - 7
An INVERSE FUNCTION reverses the action of that function [the inverse of f(x) is f^-1(x)]
Eg. If f(x) = 4 - 3x find the inverse
y = 4 - 3x
3x = 4 - y
x = (4 - y)/3
f^-1(x) = (4 - x)/3
TASK 1 - Textbook Pg13-14 Ex1E Q1e, 2e, 3, 5, 7, 8
TASK 2 - Textbook Pg15-16 Ex1F Q1d,h,l,p, 3, 5
HOMEWORK - Textbook Pg20-21 Ex1H All Qs
Eg. x is less than 5, or greater than or equal to 6
Interval notation (-∞, 5) U [6, +∞)
Set builder notation {x : x < 5, x ≥ 6}
Evaluating functions
Eg. Find f(2) when f(x) = 4x - 3
f(2) = 4(2) - 3 = 5
A COMPOSITE FUNCTION is a combination of two or more functions
Eg. If f(x) = 3x - 7 and g(x) = 2x find (f o g)(x)
(f o g)(x) = 3(2x) - 7 = 6x - 7
An INVERSE FUNCTION reverses the action of that function [the inverse of f(x) is f^-1(x)]
Eg. If f(x) = 4 - 3x find the inverse
y = 4 - 3x
3x = 4 - y
x = (4 - y)/3
f^-1(x) = (4 - x)/3
TASK 1 - Textbook Pg13-14 Ex1E Q1e, 2e, 3, 5, 7, 8
TASK 2 - Textbook Pg15-16 Ex1F Q1d,h,l,p, 3, 5
HOMEWORK - Textbook Pg20-21 Ex1H All Qs
Lesson 1...INTRODUCING FUNCTIONS
![Picture](/uploads/1/3/3/4/13343229/9434201.jpg?189)
A RELATION is a set of ordered pairs
The DOMAIN is the set of all the first numbers (x-values) of the ordered pairs
The RANGE is the set of the second numbers (y-values) in each pair
A FUNCTION is a mathematical relation such that each element of the domain of the function is associated with exactly one element of the range of the function (Vertical Line Test - a relation is a function if any vertical line drawn will not intersect the graph of that function more than once)
TASK 1 - Textbook Pg6 Ex1A
TASK 2 - Textbook Pg7 Ex1B
EXTENSION - Pg1 Investigation
The DOMAIN is the set of all the first numbers (x-values) of the ordered pairs
The RANGE is the set of the second numbers (y-values) in each pair
A FUNCTION is a mathematical relation such that each element of the domain of the function is associated with exactly one element of the range of the function (Vertical Line Test - a relation is a function if any vertical line drawn will not intersect the graph of that function more than once)
TASK 1 - Textbook Pg6 Ex1A
TASK 2 - Textbook Pg7 Ex1B
EXTENSION - Pg1 Investigation