Question

How to determine if a function is even, odd, or neither?

y = -6x^3 - 4x

I'd say that the function is odd because of the odd exponent but I'm not sure because x is being multiplied and not just cubed.

Answer 1

yes

Answer 2

a polynomial with all odd exponents is odd
hence the name (although that is not the definition)

Answer 3

You may be asked to "determine algebraically" whether a function is even or odd. To do this, you take the function and plug –x in for x, and then simplify. If you end up with the exact same function that you started with (that is, if f(–x) = f(x), so all of the signs are the same), then the function is even. If you end up with the exact opposite of what you started with (that is, if f(–x) = –f(x), so all of the "plus" signs become "minus" signs, and vice versa), then the function is odd. In all other cases, the function is "neither even nor odd".

Answer 4

source : http://www.purplemath.com/modules/fcnnot3.htm

Answer 5

your concern about the coefficients is a good one, but they make no difference in this case

Answer 6

oh i totally disagree

Answer 7

^ for polynomials.

Answer 8

Disagree with...?

Answer 9

Last question is this:
I'm supposed to write the equation that would make the parent function (solid line) transform to the related function (dashed line), here's a picture of the graph:

http://puu.sh/4Kx7R.png

I wrote

f(x) = |x^3 + 3| + 4

I'm not sure if it should be considered an absolute value or if it should, but I know that +3 is right because it moves to the left. But, since +4 is outside the absolute value, I'm not sure if it should be -4 even though it moves up.

Answer 10

question is "is the function odd"
\[f(x)=x^3+6x\] is odd,
\[f(x)=x^3+6x^2\] is not

Answer 11

for your second question, there is no absolute value at all, get rid of it and replace it by parentheses

Answer 12

Oh i might actually be mixing this up with just the end behaviour of polynomials...

Answer 13

okay, \[f(x) = (x^3 + 3) + 4\] ?

Answer 14

that looks much better

Answer 15

oh no hold the phone

Answer 16

(x+3)^3 + 4

Answer 17

\[f(x)=(x+3)^3+4\] moves left 3, up 4

Answer 18

Gotcha. Thank you!

Answer 19

we have the numbers wrong anyway... isn't it only left 2, up 3? hard to tell on that tiny graph.

Answer 20

yeah it is hard to tell for sure
i would go with 3, but i could be wrong

Answer 21

I got 3 left and 4 up.

Answer 22

now i go with 2
look at the part that looks almost horizontal
that is two units to the left of the origin

Answer 23

And you only need to write it in terms of the parent function. Not actually write the function.

If f(x) is your parent function,

f(x+2) + 3 is your transformed one.

Answer 24

the part of \(f(x)=x^3\) that is flat looking is at \((0,0)\) and the part of the other one that is flat looking is at \((-2,3)\)

Answer 25

oh crap i think it is 2

Answer 26

yeah me too, and up 3 rather than 4

Answer 27

aw man. :(

Answer 28

on line class?

Answer 29

yup, and already sent it haha.. i'm pretty sure it's fine though, i'm confident in the rest of my answers so it's cool.

Answer 30

whew!

Answer 31

If anything I can email my teacher tonight and tell her that I think I messed it up, maybe she'll give me credit for it. Thanks guys!

Answer 32

Tell her it's her fault for giving such tiny graphs :P

Answer 33

And sorry @meegan if i confused you with my post earlier... i deleted it because i was thinking of end behaviour of odd-highest power vs even-highest power polynomials... recently taught that to my precalc class and I saw the odd and even and didn't really think it through :P