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Mentoring Program Curriculum (1)
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2. Functions
Mentoring Program Curriculum (1)
/
Subjects
/
Maths AA
/
Topics
/
2. Functions
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2. Functions
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Sub-topics
•
A
relation
is any set of points which connect two variables.
•
A
function
, sometimes called
mapping
, from a set
X
X
X
to a set
Y
Y
Y
assigns to each element of
X
X
X
exactly one element of
Y
Y
Y
.
Function has different properties:
1.
Domain
is the set of values of
x
x
x
in the relation. (the set
X
X
X
)
2.1 Functions
Exponential is an inverse operation of logarithm; i.e.
a
x
=
b
⇒
x
=
log
a
b
a^x=b ⇒ x = \log_ ab
a
x
=
b
⇒
x
=
lo
g
a
b
.
Therefore, exponential function and logarithm function are an inverse of each other.
Exponentials
:
There are few exponential rules to be aware of:
2.2 Exponents and Logarithms
There are 3 types of transformations to remember.
1.
Translation by
(
a
b
)
\binom ab
(
b
a
)
to obtain
f
(
x
−
a
)
+
b
f(x-a)+b
f
(
x
−
a
)
+
b
2.
Stretch by scale factor
k
k
k
3.
Reflection
Figure 2.3.1
Graphical representation of vertical stretch by a factor of 2 (left) and horizontal transformation by 3 units and 1 unit vertically (right)
2.3 Transformation
Linear
General form:
a
x
+
b
y
+
c
=
0
ax + by + c = 0
a
x
+
b
y
+
c
=
0
Standard form:
y
=
a
x
+
b
y = ax + b
y
=
a
x
+
b
From the standard form, we have:
1.
Slope, or Gradient:
a
=
∆
y
∆
x
a = \frac {∆y}{∆x}
a
=
∆
x
∆
y
, the rate of change in
y
y
y
relative to
x
x
x
.
2.4 Polynomials
