1997962
Description
Mind Map by bubblesthelabrad, updated more than 1 year ago
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Created by bubblesthelabrad
about 9 years ago
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Algebra and Function
- Transformations
- y = f(x) + a
- Translation ( 0 , a )
- Moves the graph up a units
- Moves the graph up a units
- Translation ( 0 , a )
- y = f(x - a)
- Translation ( a , 0 )
- Subtracting a from
x shifts the graph
to the right
- Subtracting a from
x shifts the graph
to the right
- Translation ( a , 0 )
- y = -f(x) is a
reflection in
the x-axis
- y = f(-x) is a
reflection in
the y-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
- 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
- For y = |f(x)| for y
< 0 reflected in
the line of the
dotted x-axis
- y = f(x) + a
- 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 rule
connecting
the range and
domain sets
- 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
- One to One:
One X value
maps to one
Y value
- Composite Funtion
- fg(x) = f(g(x))
Put g into f
- The output
of g becomes
the input of 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
- fg(x) = f(g(x))
Put g into f
- Inverse Function
- f^-1(x)
- These can only
exist when f(x)
is a one to one
mapping
- 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)
- 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.
- f^-1(x)
- A function is defined by:
- Modulus Function
- |x| = x if x > 0
- |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 or x > a
- |x -a | = x - a for x >= a
- |x - a| = -(x - a) = a - x for x
- |x - a| = -(x - a) = a - x for x
- |x - b| <= a = -a < x - b < a
- |x - b| >= a = b - a < x < a - b
- |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
- |f(x)| = |g(x)| <==>
(f(x))^2 = (g(x))^2
- Mod graphs will never go below the x-axis
- |x| = x if x > 0
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