precalculus
basic rules of functions
basic rules of functions
what is this called?
THE RANGE
what toolkit function is this?
CUBE ROOT
f(x)=cube root of x
what toolkit function is this?
SQUARE ROOT
f(x)=square root of x
x >= 0
what toolkit function is this?
RECIPROCAL SQUARED
f(x)=1/(x squared)
what toolkit function is this?
RECIPROCAL
f(x)=1/x
what toolkit function is this?
CUBIC
f(x)=x cubed
what toolkit function is this?
QUADRATIC
f(x)=x squared
what toolkit function is this?
ABSOLUTE VALUE
f(x)=|x|
what toolkit function is this?
IDENTITY
f(x)=x
what toolkit function is this?
CONSTANT
f(x)=c
c is constant
?
YES
PASSES THE VERTICAL LINE TEST
?
NO
FAILS THE VERTICAL LINE TEST
what's this called?
4th QUADRANT
what's this called?
3rd QUADRANT
what's this called?
1st QUADRANT
what's this called?
2nd QUADRANT
what kind of function is this?
ONE-TO-ONE
PASSES THE HORIZONTAL LINE TEST
what's this called?
the RANGE
what toolkit function is this?
CUBE ROOT
what toolkit function is this?
CUBIC
f(x)= x squared
LINEAR FUNCTION
f(x)=mx+b
g(x)=f(x+m)
SHIFT LEFT by m
g(x)=f(x-m)
SHIFT RIGHT by m
g(x)=f(x)+m
SHIFT UP by m
g(x)=f(x)-n
SHIFT DOWN by m
g(x)=m*f(x)
STRETCH VERTICALLY by m
g(x)=f(m*x)
COMPRESS HORIZONTALLY by 1/m
g(x)=f(m*x), m<1
STRETCH HORIZONTALLY
g(x)=f(x)*m, m<1
COMPRESS VERTICALLY
g(x)= -(f(x))
REFLECTION ACROSS X AXIS
up becomes down and vice versa
g(x)=f(-x)
REFLECTION ACROSS Y AXIS
left becomes right and vice versa
f(x)=mx+b
LINEAR FUNCTION
Linear Function
f(x)=mx+b
N
THE SET OF ALL NATURAL NUMBERS
{1,2,3,4,...}
.
THE SET OF WHOLE NUMBERS
{0,1,2,3,4,...}
Z
THE SET OF INTERGERS
{...,-2,-1,0,1,2,...}
Q
THE SET OF RATIONAL NUMBERS
{p/q: p and q are integers, q does not equal 0}
I
THE SET OF IRRATIONAL NUMBERS
{x: x cannot be expressed as a ratio of 2 integers}
R=?U?
R=QUI
THE SET OF ALL REAL NUMBERS
.
empty set {}
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Cartes-fiches
LINEAR FUNCTION
f(x)=mx+b
g(x)=f(x+m)
SHIFT LEFT by m
g(x)=f(x-m)
SHIFT RIGHT by m
g(x)=f(x)+m
SHIFT UP by m
g(x)=f(x)-n
SHIFT DOWN by m
g(x)=m*f(x)
STRETCH VERTICALLY by m
g(x)=f(m*x)
COMPRESS HORIZONTALLY by 1/m
g(x)=f(m*x), m<1
STRETCH HORIZONTALLY
g(x)=f(x)*m, m<1
COMPRESS VERTICALLY
g(x)= -(f(x))
REFLECTION ACROSS X AXIS
up becomes down and vice versa
g(x)=f(-x)
REFLECTION ACROSS Y AXIS
left becomes right and vice versa
f(x)=mx+b
LINEAR FUNCTION
Linear Function
f(x)=mx+b
N
THE SET OF ALL NATURAL NUMBERS
{1,2,3,4,...}
.
THE SET OF WHOLE NUMBERS
{0,1,2,3,4,...}
Z
THE SET OF INTERGERS
{...,-2,-1,0,1,2,...}
Q
THE SET OF RATIONAL NUMBERS
{p/q: p and q are integers, q does not equal 0}
I
THE SET OF IRRATIONAL NUMBERS
{x: x cannot be expressed as a ratio of 2 integers}
R=?U?
R=QUI
THE SET OF ALL REAL NUMBERS
.
empty set {}
Q intersection I=?
empty set {}
.
A BELONGS TO SET B
.
A IS NOT IN SET B
.
INCLUSION
A IS A SUBSET OF B
all elements of A are in B
.
INTERSECTION
THE SET OF ELEMENTS IN BOTH A AND B
{x: x€A and x€B}
the overlap of elements from A and B
AUB
UNION
THE SET OF ALL ELEMENTS FROM BOTH A AND B
{x: x€A OR x€B}
what is this called?
THE DOMAIN
what is this called?
THE RANGE
what toolkit function is this?
CUBE ROOT
f(x)=cube root of x
what toolkit function is this?
SQUARE ROOT
f(x)=square root of x
x >= 0
what toolkit function is this?
RECIPROCAL SQUARED
f(x)=1/(x squared)
what toolkit function is this?
RECIPROCAL
f(x)=1/x
what toolkit function is this?
CUBIC
f(x)=x cubed
what toolkit function is this?
QUADRATIC
f(x)=x squared
what toolkit function is this?
ABSOLUTE VALUE
f(x)=|x|
what toolkit function is this?
IDENTITY
f(x)=x
what toolkit function is this?
CONSTANT
f(x)=c
c is constant
?
YES
PASSES THE VERTICAL LINE TEST
?
NO
FAILS THE VERTICAL LINE TEST
what's this called?
4th QUADRANT
