Function and Graph - Extended

8/12/2019 Function and Graph - Extended

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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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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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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)

Function and Graph - Extended

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