Even function, odd function or neither

[lewch45]

I kind of understand the concept of determining this but I'm confusing myself. I have these 3 equations and I need to determine if they're even, odd or neither.
They are:

1. G(x)=2x^5-10

2. T(x)=IxI+2...this I'm pretty sure is even because of the absolute value

3. z(x)=x^3/x^2+1

Can someone please help? Thanks!

 

[Unco]

For the first one,

Determine G(-x):

G(-x) = 2(-x)^5 - 10
G(-x) = -2x^5 - 10
because with an odd exponent the negative stays

This is not the same as G(x) (which was 2x^5-10), so G(x) is not even.

Compare with -G(x):

-G(x) = - [2x^5-10]
-G(x) = -2x^5 + 10

This isn't G(-x) (the 10 is positive whereas is was negative before) so G(x) is not odd either.

(You're spot on for the second one, by the way.)