math for 800 09 functions
Post on 30-Jul-2015
101 Views
Preview:
TRANSCRIPT
DEFINITION OF FUNCTION
A function f from a set
A to a set B is a
relation that assigns to
each element x in the
set A exactly one
element on the set B.
Set A
Set B
DOMAIN AND RANGE
The set A is the
domain of the function f, and the
set B contains the
range.
Set A Set B
REPRESENTING A FUNCTION
Some algebraic expressions are called
functions and are represented by f (x).
The symbol “f (x)” do not represent a
product; is merely the symbol for an
expression, and is read “f of x”.
Graphically: By points on
a graph in a coordinate
plane.
REPRESENTING A
FUNCTION
The symbol f (x)
corresponds to the y−value
for a given x, y = f(x).
GRAPH OF A FUNCTION
The graph of a function f is the
collection of ordered pairs
(x, f(x)) such that x is in the
domain of f.
x : distance from y-axis.
f(x) : distance from x-axis. ,x f x
INTERCEPTS OF A FUNCTION
To find the x−intercept(s), let
y = f (x) = 0 and solve the
equation for x.
To find the y−intercept(s), let
x = 0 and solve the equation
for y. 0y f x
y
x
y
x
y
x
Symmetry to the y-axis Symmetry to the origin Symmetry to the x-axis
(Not a function)
(-x, y) (x, y)(x, y)
(-x, -y)
(x, y)
(x, -y)
SYMMETRY OF A FUNCTION
LINEAR FUNCTION
A linear function is defined by , where m and
b are real numbers.
m: slope of the line
b: y−intercept
f x mx b
y
x
b
rise
run
y mx b
GRAPH A LINEAR INEQUALITY
1.Rearrange the
equation so " " is on the left and
everything else on
the right.
2 3 6x y
3 2 6
22
3
y x
y x
GRAPH A LINEAR INEQUALITY
2. Plot the "y=" line (a solid line for
y≤ or y≥, and a
dashed line for
y< or y>).
22
3y x
22
3y x
GRAPH A LINEAR INEQUALITY
3. Shade above the
line for a "greater
than" (y> or y≥) or
below the line for a
"less than" (y< or y≤).
22
3y x
QUADRARTIC FUNCTION
A quadratic function is a
function described by an
equation that can be written in
the form:
2f x ax bx c 0a where
vertex(Xv, Yv)
x
y
VERTEX
The graph of any quadratic
function is a parabola.
24
2 4v v
b ac bX Y
a a
MINIMUM
If a > 0 the parabola
opens upwards and
the vertex is the lowest
point of the parabola
(minimum).
2f x ax bx c Vertex (minimum)
MAXIMUM
If a < 0 the parabola
opens downwards and
the vertex is the highest
point of the parabola
(maximum).
Vertex (maximum) 2f x ax bx c
f(x)=(x-1)^2+3
f(x)=-(x+1)^2-3
Series 1
-12 -10 -8 -6 -4 -2 2 4 6 8 10 12 14 16
-6
-4
-2
2
4
6
8
x
y
vertex(maximum)
a < 0
vertex(minimum)
a > 0
2f x ax bx c
EXTREME VALUES
SPECIAL FUNCTIONS
Special symbols are used
to represent some
defined functions.
2 21 1f x x x x
, , # #
c ca b a b
Z a b c a b cb c b c
top related