Math help (2 Viewers)

[Fawun]

Re: Math help (Because Carrot made me do this)

Classify the following functions f(x) as odd, even or neither.



What do I do?

 

[Carrotsticks]

Re: Math help (Because Carrot made me do this)

Classify the following functions f(x) as odd, even or neither.



What do I do?

Therefore odd.

Just make f(x) become f(-x) and look at what happens to the function.

It it's the exact same thing, then even.

If the same thing, but with a minus in front (like here), then odd.

If neither, then neither.

 

[kazemagic]

Re: Math help (Because Carrot made me do this)

2 things u need to rmbr
Even functions:
f(-x)=f(x) (when subbed in a negative pronumeral, the equation still stays the same)

Odd functions:
f(-x)=-f(x) (when subbed in a negative pronumeral, the equation becomes negative)

Wow ur going fast, last time i saw u, u were doing quadratics

 

[Fawun]

Re: Math help (Because Carrot made me do this)

2 things u need to rmbr
Even functions:
f(-x)=f(x) (when subbed in a negative pronumeral, the equation still stays the same)

Odd functions:
f(-x)=-f(x) (when subbed in a negative pronumeral, the equation becomes negative)

Wow ur going fast, last time i saw u, u were doing quadratics

what? where?

Therefore odd.

Just make f(x) become f(-x) and look at what happens to the function.

It it's the exact same thing, then even.

If the same thing, but with a minus in front (like here), then odd.

If neither, then neither.

Why did you put the minus sign in front of the x but not for the x squared part of the denominator?

 

[Carrotsticks]

Re: Math help (Because Carrot made me do this)

what? where?



Why did you put the minus sign in front of the x but not for the x squared part of the denominator?

Because if I replace the x with -x, then I get (-x)^2, which is still x^2.

 

[kazemagic]

Re: Math help (Because Carrot made me do this)

what? where?



Why did you put the minus sign in front of the x but not for the x squared part of the denominator?

HSN thread

 

[Fawun]

Re: Math help (Because Carrot made me do this)

Because if I replace the x with -x, then I get (-x)^2, which is still x^2.

Okay so let me get this straight.

If the function is the same as the question, then it's even
If it's different from the question, then it's odd

Am I right?

 

[Carrotsticks]

Re: Math help (Because Carrot made me do this)

Okay so let me get this straight.

If the function is the same as the question, then it's even
If it's different from the question, then it's odd

Am I right?

Not really.

If I replace X with (-X) and I get the exact same thing, then it's even.

If I replace X with (-X) and I get the same thing EXCEPT it has minus in front, then it's odd.

If I replace X with (-X) and I get neither of the above cases, then it is neither.

 

[kazemagic]

Re: Math help (Because Carrot made me do this)

Okay so let me get this straight.

If the function is the same as the question, then it's even
If it's different from the question, then it's odd

Am I right?

When subbed in a negative pronumeral, and the equations stays the same, it is an even
When subbed in a negative pronumeral, and the equation stays the same and becomes negative, it is an odd
When subbed in a negative pronumeral, and the equation becomes something different, it is neither

fawun bro why dont u listen to ur teacher during class time

 

[Fawun]

Re: Math help (Because Carrot made me do this)

Not really.

If I replace X with (-X) and I get the exact same thing, then it's even.

If I replace X with (-X) and I get the same thing EXCEPT it has minus in front, then it's odd.

If I replace X with (-X) and I get neither of the above cases, then it is neither.

In front of where? the x? or any number with a minus in front?

When will there be a case where it will be a neither? doesn't a question have to have a plus or a minus? idgi.

So let's say for this question:



I got:




Is this right so far? What do I do next? Do I like expand it or something?

 

[Aykay]

Re: Math help (Because Carrot made me do this)

Anything to an even power is positive.
So (-x)^2 = x^2 in the same way that (-2)^4 = 2^4.

 

[Fawun]

Re: Math help (Because Carrot made me do this)

When subbed in a negative pronumeral, and the equations stays the same, it is an even
When subbed in a negative pronumeral, and the equation stays the same and becomes negative, it is an odd
When subbed in a negative pronumeral, and the equation becomes something different, it is neither

fawun bro why dont u listen to ur teacher during class time

Okay I understood those parts thanks. She explains things too quickly and i'm too embarrassed to ask a question since everyone else is smarter than me and will think i'm dumb lol.

 

[Carrotsticks]

Re: Math help (Because Carrot made me do this)

In front of where? the x? or any number with a minus in front?

When will there be a case where it will be a neither? doesn't a question have to have a plus or a minus? idgi.

So let's say for this question:



I got:




Is this right so far? What do I do next? Do I like expand it or something?

When I say it has a minus in front, I mean that it's the EXACT same function, but multiplied by -1.

So for example if:



Then -f(x) is:



In your case, you have



But notice, that's NOT the original function. On top of that it's NOT the same thing as the original function, but with a -1 chucked in front of it:



So therefore, not odd and not even, and thus neither.

 

[Sy123]

Re: Math help (Because Carrot made me do this)

In front of where? the x? or any number with a minus in front?

When will there be a case where it will be a neither? doesn't a question have to have a plus or a minus? idgi.

So let's say for this question:



I got:




Is this right so far? What do I do next? Do I like expand it or something?

You can do two things, expand:


Therefore function is neither. What classifies a function of being odd or even is:

If a function is odd, then if you rotate it 360 degrees about the origin, the function is the exact same
If a function is even, then it it symetrical about the y axis.

This is how people derive the rules for odd and even functions, you dont need to know how they did it, but you need to know why an even function is an even function. If we test whether f(x)=f(-x), if its true then function is symmetrical hence it is even.

If its neither, it has neither properties of an even or odd function.

When carrot means it has a minus in front, he means:

Hence odd:

If we translate this:

If I replace X with (-X) and I get the same thing EXCEPT it has minus in front, then it's odd.

'If I replace x with (-x), i.e. evaluating f(-x), and I get the same thing [f(x)] but with a minus in front [-f(x)]'

 

[Fawun]

Re: Math help (Because Carrot made me do this)

When I say it has a minus in front, I mean that it's the EXACT same function, but multiplied by -1.

So for example if:



Then -f(x) is:

Why is it -f(x)? isn't it f(-x)?

In your case, you have

How did you get ? Did you just cancel out the negatives? or did you expand it?

But notice, that's NOT the original function. On top of that it's NOT the same thing as the original function, but with a -1 chucked in front of it:


So therefore, not odd and not even, and thus neither.

Wait what? why did you chuck a -1 in front of it?

 

[Carrotsticks]

Re: Math help (Because Carrot made me do this)

Why is it -f(x)? isn't it f(-x)?



How did you get ? Did you just cancel out the negatives? or did you expand it?



Wait what? why did you chuck a -1 in front of it?

That's the idea. Since -f(x) IS equal to f(-x), then it is an odd function.

I got the x(x+1) by multiplying the minus inside.

OKok here let me draw a diagram for you. Give me a few moments.

 

[Fawun]

Re: Math help (Because Carrot made me do this)

You can do two things, expand:

Why didn't you put a minus in front of the second function? I know that (-x)^2 is the same as x^2 but why didn't you put -x? so then it becomes x^2-x?

When carrot means it has a minus in front, he means:

So basically f(-x) is the same as -f(x)?

 

[Sy123]

Re: Math help (Because Carrot made me do this)

Why didn't you put a minus in front of the second function? I know that (-x)^2 is the same as x^2 but why didn't you put -x? so then it becomes x^2-x?



So basically f(-x) is the same as -f(x)?

I just expanded what you gave me as f(-x)

If f(-x)=-x(-x-1)
f(-x)=x^2+x

When we sub in -x, its like subbing in any other pronumeral, for example

f(x)=x(x-1)
f(a)=a(a-1)


Putting a minus in front of the function means this -f(x)
So if

Now lets have a look at -f(x), does it look identical to anything? No, therefore its not odd
Does f(-x) look like anything? No, therefore it isnt even either.

Also me explaining what carrot said was a failure on my part. But basically yeah if f(-x)=-f(x) then its odd

 

[Carrotsticks]

Re: Math help (Because Carrot made me do this)

Some things are better explain irl.

 

[kazemagic]

Re: Math help (Because Carrot made me do this)

Here are my some of my notes on this