1.) Even and Odd Functions
•
A function is said to be even if
𝑓(𝑥) = 𝑓(−𝑥).
3.) One to One Function
•
Example: 𝑦 = 𝑥 2
𝑓(𝑥) = 𝑥 2 ; 𝑓(−𝑥) = (−𝑥)2 = 𝑥 2
A function is one to one if for
every x in X there exist an
element y in Y such that for 𝑥1 ≠
𝑥2 → 𝑓(𝑥1 ) ≠ 𝑓(𝑥2 ).
Example: all functions of degree 1
•
A function is said to be odd if
𝑓(−𝑥) = −𝑓(𝑥).
Example: 𝑦 =
1
𝑥
𝑓(−𝑥) =
1
−( )
𝑥
=
1
−𝑥
=−
1
𝑥
; −𝑓(𝑥) =
1
−
𝑥
Thus, 𝑦 = 𝑥 2 is an even function and 𝑦 =
1
is an odd function.
𝑥
4.) Onto functions
2.) Increasing and Decreasing Functions
•
•
A function is said to be increasing
if as x values increases, y values
also increases
Example: 𝑦 = 2𝑥 + 1
•
A function is said to be
decreasing if as x values
increases, y values decreases.
1
𝑥
Example: 𝑦 = , 𝑥 ≠ 0
A function is onto if for every y in
Y there is an element x in X such
that 𝑦 = 𝑓(𝑥).
5.) Functions defined piecewise
•
A function is defined piecewise if
for every specified domain there
is a corresponding y values.
Example:
1, 𝑥 > 0
𝑓(𝑥) = [ 0, 𝑥 = 0 ]
−1, 𝑥 < 0
6.) Linear Functions
•
A linear function is a function of
degree 1.
•
𝑎𝑥 + 𝑏𝑦 + 𝑐 = 0
•
𝑦 = 𝑚𝑥 + 𝑏
Example:
𝑦 =𝑥+1
𝑦 = −2𝑥 + 5
𝑦=𝑥+
1
2
7.) Quadratic Functions
•
A quadratic function is a function
of degree 2.
•
𝑓(𝑥) = 𝑎𝑥 2 + 𝑏𝑥 + 𝑐
•
The graph is a parabola.
Examples:
𝑦 = 𝑥2
𝑦 = −2𝑥 2 − 1
𝑦 = 𝑥 2 − 4𝑥 + 4