relations and functions (1 Viewer)

[*girl04*]

hey we are currently doing realations and functions and we have to find out whether a function is odd or even, using a formula it looks something like this f(-x) = x2 or something anyway if your following can anyone give me examples on how your meant to use it@ and im not getting the domain or range thing. like i understand the x values are domaina nd y range but doing calulations n stuff thanks for any help!

 

[:: ck ::]

wrong forum... anyways

odd : f(-x) = -f(x)
even : f(-x) = f(x)

 

[Xayma]

You use it a fair bit in curve sketching if you can see it quickly, because you can just either mirror it or flip it over at x=0.

 

[*girl04*]

Originally posted by :: ryan.cck ::
wrong forum... anyways

odd : f(-x) = -f(x)
even : f(-x) = f(x)

i can sort of do it but i just dont get why i make the x's negative
which froum am i supposed to post in?

 

[Affinity]

graph

y=x
y=x^2 (x squared)
y=x^3
y=x^4
y=x^5

more if you have time.

notice if you rotate the graphs of the odd powered x's about the origin for 180 degrees, you get the same graph. That's basically what odd functions are, they are symmetric about the origin.

now look at the graph for the even powers, if you reflect the graph about the y axis, it looks the same. This is what makes a function even (symmetric about the y axis)

expressed in equations, it's what ryan posted.


to use it.. suppose you want to graph an even function

say y = 1 / (1 + x^2)

you will just need to calculate/ find data about the graph for positive x, graph it, then draw the reflection about the y axis to give the graph for negative x.

for odd functions, say [e^x - (1/e^x)]/2

graph the graph for positive x and rotate it by 180 degrees about (0,0) will give you the other part of the graph.

in HSC it's also used in integration problems, if you are asked to find:
/a
| f(x) dx
/b

if f(x) is odd, then it is 0.

if f(x) is even, the integral will equal

/a
| 2*f(x) dx
/0

 

[Heinz]

Originally posted by *girl04*

which froum am i supposed to post in?

Relations and functions is a 2u topic. You should really post in the mathematics forum and not the ext 2. I dont see the big deal though, maths is maths.

 

[*girl04*]

i do 3u maths but im in yr 11 so i just picked and posted

 

[KeypadSDM]

Originally posted by Affinity
in HSC it's also used in integration problems, if you are asked to find:
/a
| f(x) dx
/b

if f(x) is odd, then it is 0.

if f(x) is even, the integral will equal

/a
| 2*f(x) dx
/0

Ahem, you forgot to say b = -a

 

[Xayma]

Or for area:
/a
| f(x) dx
/-a

=
/a
2| f(x) dx
/0

if f(x) is even or odd.

 

[Calculon]

To girl04

How come you keep posting in the yr 12 forums, you're in yr 11

 

[Affinity]

because you get more answers here

 

[ameh]

Originally posted by *girl04*
i can sort of do it but i just dont get why i make the x's negative
which froum am i supposed to post in?

u sub da x in, then u times by -1...u make them negative bcos its an exponential thingo and cubed and squared usually r either neg or pos...i think....well i hav a test for this on wed and i shud noe more than this....sorry!

 

[Maianbarian]

You make the 'x's negative because that is the definition of odd and even functions. for example:

f(x)=x^2
therefore f(-x)=(-x)^2

now a negative by a negative gives a positive therefore:
f(-x) = x^2
=f(x) therefore f(x) is even

or
g(x)=x^3
g(-x)=(-x)^3
now 3 negatives give a negative so:
g(-x)=-x^3
=-g(x)

therefore g(x) is odd.

Those are two very simple ones but the same principle and method applies to all. Of course it is often easier just to look at the graph of f(x) as has already been explained.

 

[Merforga]

simple way :

replace x with -x. If its the same then its even, if its the negative of the previous function its odd ^^