 # Algebra and Function

Mind Map by , created almost 5 years ago

## A-Level Mathematics (Core 3) Mind Map on Algebra and Function, created by bubblesthelabrad on 02/10/2015. 23 1 0  Created by bubblesthelabrad almost 5 years ago
AS Biology Unit 1
Biological Psychology - Stress
Integration and differentiation BASICS ONLY
Relationships Anthology
4. Without application in the world, the value of knowledge is greatly diminished. Consider the claim with respect to two areas of knowledge.
Decision 1
TYPES OF DATA
HISTOGRAMS
AS Pure Core 1 Maths (AQA)
STEM AND LEAF DIAGRAMS
Algebra and Function
1 Transformations
1.1 y = f(x) + a
1.1.1 Translation ( 0 , a )
1.1.1.1 Moves the graph up a units
1.2 y = f(x - a)
1.2.1 Translation ( a , 0 )
1.2.1.1 Subtracting a from x shifts the graph to the right
1.3 y = -f(x) is a reflection in the x-axis
1.3.1 y = f(-x) is a reflection in the y-axis
1.4 y = af(x) is a stretch in the y direction by a
1.4.1 y = f(ax) is a stretch in the x direction be a^-1
1.5 For y = f(|x|) for x > 0 and reflects in y to the right
1.5.1 For y = |f(x)| for y < 0 reflected in the line of the dotted x-axis
2 Functions
2.1 A function is defined by:
2.1.1 A rule connecting the range and domain sets
2.1.2 For each member of the domain, there is only one range value
2.2 A Function y = f(x)
2.2.1 One to One: One X value maps to one Y value
2.2.2 Many to One: More than one value of X maps to one value of Y
2.3 Composite Funtion
2.3.1 fg(x) = f(g(x)) Put g into f
2.3.1.1 The output of g becomes the input of f
2.3.2 Can only be formed in the example of fg(x). When the range of g is in the domain of f
2.4 Inverse Function
2.4.1 f^-1(x)
2.4.1.1 These can only exist when f(x) is a one to one mapping
2.4.2 The range of f is the domain of f^-1 and vice versa
2.4.2.1 The graph y=f(x) is the reflection of y=f^-1(x)
2.4.3 To turn f(x) into f^-1(x). Replace the x with y's and vice versa then make y the subject.
3 Modulus Function
3.1 |x| = x if x > 0
3.1.1 |x| = -x if x < 0
3.2 |x| < a = -a < x < a
3.2.1 |x| > a = x < -a or x > a
3.3 |x -a | = x - a for x >= a
3.3.1 |x - a| = -(x - a) = a - x for x
3.4 |x - b| <= a = -a < x - b < a
3.4.1 |x - b| >= a = b - a < x < a - b
3.5 |f(x)| = a <==> f(x) = a or f(x) = -a
3.5.1 |f(x)| = |g(x)| <==> (f(x))^2 = (g(x))^2
3.6 Mod graphs will never go below the x-axis