Question

Please tell me if f(x) = x^3 + 0.04x^2 + 3 is odd, even or niether (then tell me how you found out)

Answer 1

Hey jim!!

Answer 2

hey

Answer 3

Hint: if f(-x) = f(x), then the function is even

Answer 4

I'm doin' good in class. Your help on my math packet got me some good brownie points :)

Answer 5

if f(-x) = -f(x), then the function is odd

Answer 6

right. But I'm not sure how to show it

Answer 7

so first, let's find f(-x)

Answer 8

does f(-x) = -x^3 -0.04x + 3

Answer 9

f(x) = x^3 + 0.04x^2 + 3


f(-x) = (-x)^3 + 0.04(-x)^2 + 3


f(-x) = -x^3 + 0.04x^2 + 3

Answer 10

keep in mind that (-x)^2 = x^2

Answer 11

so does f(-x) = f(x)???

Answer 12

but not (-x)^3

Answer 13

(-x)^3 = (-x)*(-x)*(-x) = -x^3

Answer 14

so f(-x) does not = f(x)

Answer 15

yep

Answer 16

which means that f is not an even function

Answer 17

so it's neither ?

Answer 18

now what about f(-x) = -f(x)?

Answer 19

F IS NOT EVEN A FUNCTION? Omg dude

Answer 20

lol

Answer 21

huh

Answer 22

just kidding around

Answer 23

f(-x) = -x^3 - 0.04x - 3?

Answer 24

we can refer to f(x) as f, I've seen it plenty of times

Answer 25

I'm not sure how to show f(-x) = -f(x)

Answer 26

negate everything in f(x) to get -f(x)

Answer 27

-f(x) = -1*f(x)

Answer 28

So if f(x) = x^3 + 0.04x^2 + 3, then -f(x) = -1*f(x) = -1(x^3 + 0.04x^2 + 3)

Answer 29

then you distribute and simplify

Answer 30

neither instantly and with your eyeballs

Answer 31

so it would be -x^3+0.04x^2+3 = -x^3-0.04x^2-3. so it is neither.

Answer 32

\[f(x) = x^3 + 0.04x^2 + 3 \] has both even and odd powers, so neither

Answer 33

yep you got it

Answer 34

thanks jim :)

Answer 35

yw