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1997962
Algebra and Function
Descrição
A-Level Mathematics (Core 3) Mapa Mental sobre Algebra and Function, criado por bubblesthelabrad em 10-02-2015.
Sem etiquetas
alegbra
functions
core 3
maths
aqa
alevel
mathematics
core 3
a-level
Mapa Mental por
bubblesthelabrad
, atualizado more than 1 year ago
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Criado por
bubblesthelabrad
mais de 9 anos atrás
28
1
0
Resumo de Recurso
Algebra and Function
Transformations
y = f(x) + a
Translation ( 0 , a )
Moves the graph up a units
y = f(x - a)
Translation ( a , 0 )
Subtracting a from x shifts the graph to the right
y = -f(x) is a reflection in the x-axis
y = f(-x) is a reflection in the y-axis
y = af(x) is a stretch in the y direction by a
y = f(ax) is a stretch in the x direction be a^-1
For y = f(|x|) for x > 0 and reflects in y to the right
For y = |f(x)| for y < 0 reflected in the line of the dotted x-axis
Functions
A function is defined by:
A rule connecting the range and domain sets
For each member of the domain, there is only one range value
A Function y = f(x)
One to One: One X value maps to one Y value
Many to One: More than one value of X maps to one value of Y
Composite Funtion
fg(x) = f(g(x)) Put g into f
The output of g becomes the input of f
Can only be formed in the example of fg(x). When the range of g is in the domain of f
Inverse Function
f^-1(x)
These can only exist when f(x) is a one to one mapping
The range of f is the domain of f^-1 and vice versa
The graph y=f(x) is the reflection of y=f^-1(x)
To turn f(x) into f^-1(x). Replace the x with y's and vice versa then make y the subject.
Modulus Function
|x| = x if x > 0
|x| = -x if x < 0
|x| < a = -a < x < a
|x| > a = x < -a or x > a
|x -a | = x - a for x >= a
|x - a| = -(x - a) = a - x for x
|x - b| <= a = -a < x - b < a
|x - b| >= a = b - a < x < a - b
|f(x)| = a <==> f(x) = a or f(x) = -a
|f(x)| = |g(x)| <==> (f(x))^2 = (g(x))^2
Mod graphs will never go below the x-axis
Anexos de mídia
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