Question

Determine algebraically whether the function is even, odd, or neither even nor odd.

Answer 1

Medal rewarded

Answer 2

@Yttrium

Answer 3

How do you differentiate function that is even, odd or neither even nor odd?

Answer 4

I dont know, thats why im asking.
I am posting a few questions on a practice exam that i dont know the answers two, its doesn't count for anything, just a way to study.

Answer 5

Could you tell me what the answer is and why?

Answer 6

Please, im kind of in a hurry.

Answer 7

Simplify f(-x).

If f(-x)=f(x), then it is even.
If f(-x)=-f(x), then it is odd.

If f(-x) is not equal to either of those, then it's neither.

Answer 8

Just plug in -x into the equation, and see if it will come up with this conditions:
1. Direct opposite. Hence, that is odd.
2. The same. Hence, that is even.
3. Not direct opposite nor same. Neither even nor odd.

Answer 9

Do you get it now @MandyNeedsHelp ?

Answer 10

Is it odd?

Answer 11

No. Simplify first the expression. Find the LCD to avoid fractions.

Answer 12

Thats why i cant find this one because i dont know how with a fraction

Answer 13

Wait - are we looking at the same problem, @Yttrium ?

f(x)=x+4/x ??

f(-x)=-x+4/(-x) = -x-4/x=-(x+4/x)??

Answer 14

Multiply this by x, to cancel the denom x in the second term, right?
\[x [x+\frac{ 4 }{ x }]\]
Hence,
\[f(x)x^2+4\]
Now, insert (-x) and see what will happen.
I think so @DebbieG

Answer 15

I mean \[f(x) = x^2 +4\]

Answer 16

Wait, is this neither?

Answer 17

It's actually even. :)

Answer 18

Wanna know why?

Answer 19

yes i do lol

Answer 20

You can't multiply a function by x!!

You can multiply it by x/x.

but if you multiply it by x, it's a DIFFERENT function than what you started with.

Answer 21

The fraction shouldn't be a problem for determining oddness or evenness, just see what I did above.

But, if you don't like the fraction, then by all means, write over LCD of x:

\(\large f(x)=\dfrac{x^2+4}{x}\)

Then again:
\(\large f(-x)=\dfrac{(-x)^2+4}{-x}=\dfrac{x^2+4}{-x}=-\left(\dfrac{x^2+4}{x}\right)=-f(x)\)

Answer 22

Just look at the graph:
https://www.desmos.com/calculator/kt2ih5gevg

Odd, for sure.

Answer 23

Compare to \(y=x^2+4\):
https://www.desmos.com/calculator/74ryzng7e7

Not the same function.

Answer 24

Oh I forgot to write the denom. That's what I really wanna say. HAHA. Thanks @DebbieG

Answer 25

Thank you both so much!!!

Answer 26

you're welcome. :)