function and graph - extended
TRANSCRIPT
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FUNCTION AND GRAPH
Chapter 1.2 PROPERTIES OF FUNCTION
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Function Lets assume we have a function :
Y = x2 This function can be written as:
f(x) = x2
Horizontal line
In graph willrepresent
x axis and
Vertical line will
represent f(x)
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Finding graph of a function
f(x) = x
2
Now, if
x = 0; thn f(0) = (0)2 =0
x = 1; thn f(1) = (1)2 =1
x = 2; thn f(2) = (2)2 =4 x = 3; thn f(3) = (3)2 =9
.
x = -1; thn f(-1) = (-1)2 =1
x = -2; thn f(-2) = (-2)2 =4 x = -3; thn f(-3) = (-3)2 =9
..
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Graph co-ordinates
So, the coordinates of x2
are, (x, f(x))
=(0,0), (1,1), (2,4), (3, 9), (-1,1), (-2,4), (-3, 9) as
far as u can go
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DOMAIN
u can find out graph of any function u are givenusing the method I just showed.
Assume a value of x and find out the value of f(x)
against tht value.
f(x) = x2x = 3; thn f(3) = (3)2 =9
Here for a function like x2u can choose any value of x.
HOWEVER,,, some functions has limitation, u can not just put any
value for x. For example :
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How to find domain
f(x) =
Value of x MUST
BE POSITIVE;
f(x)=
Value of x MUST NOT
BE ZERO;
1. Value inside square-root must be POSITIVE(cz square-root cant process negative numbers
2. Denominator must not be ZERO
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Example:
Find the Domain of the following equations:y2 + x2= 25
Solution:
y2 + x2= 25y2 = 25 - x2
y = +
f(x)= | |
so,25 - x2 > 0
x2
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..continuation of previous slide
value of x will be equal to 5 or less thn 5 andmore thn -5 can e written as
-5
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..continuation of previous slide
HINTS:
FOR,
FOR, -
find f(5), f(4), f(3), f(2), f(1), f(0), f(-1), f(-2), f(-3), f(-4), f(-5) For and
draw the graph AND
find f(5), f(4), f(3), f(2), f(1), f(0), f(-1), f(-2), f(-3), f(-4), f(-5) For - anddraw the graph
U can chk previous slide no 3 for more details
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THE GRAPH OF THE MATH WILL LOOK
LIKE THIS:
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Summary
Find f(x) from y2
+ x2
= 25 Which is f(x)= | |
Find domain of x which is -5
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Properties of graph.
x , x2
, x3,
, 1/x, sin x, cos x, tanx,
All of them has different type of shapes whn u
convert them into graph.
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JUST REMEMBER THIS SHAPES OF GRAPHSACCORDING TO THEIR EQUATIONS.
ONCE U SEE AN EQUATION, IF CAN REMEMER
THE PROPERTIES , U CAN IMAGINE HOW THEGRAPH WILL LOOK LIKE..
SO JUST FIND DOMAIN & RANGE, put them into
the graph and draw the shape..u dnt hav to go toevery single coordinate to find the shape.
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DOMAIN & RANGE
IF f(x)=
THN, domain : -5
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HOMEWORK
Find domain range and graph for :a.) y = 1/(x-5)
b) y = (1/x) -5
c) y2= x2-4
d) y = 9 - x2
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Tricky Example:
f(x) = (x
2
- 4) / (x-2) f(x) = (x2- 4) / (x-2)
= (x - 2) (x+2) / (x-2)
= x + 2
so, f(x) = x+2
this is the tricky part.. u can put any value for x when f(x) = x+2;
BUT..
our main function is f(x) = (x2- 4) / (x-2)
HERE, x MUST NOT BE 2. cz if x = 2 thn denominator is is 2-2 = 0.
so... even though f(x) = x+2 , domain is any value of X except 2.
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Example: DRAW THE GRAPH of f(x)
this math, there are 3 conditions of f(x)according to the value x.
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solution:
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..continuation of previous slide
so...
f(-3) = 0
f (-2) = 0
f(-1) = 0
f(0) = 1f( 1) = 0
f(2) =2
f(3) =3
f(4) = 4
....
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TRY these at home
find the graph off(x) = tanx (hints: tanx =sinx/cosx ; so cosx must NOT be 0)
((hints: x-1 > 0 so, x > 1...so find out f(1),
f(2)..till f() f(5) or, f(6)