Question

Determine if the function is odd, even, or neither.
h(x)=x^2-x^12
(^means raised. So x raised to the second, and x raised to the 12th) Thank you

Answer 1

so find f(-x) = (-x)^2 - (-x)^12 since both terms are even powers the result is
f(-x) = x^2 - x^12

so f(-x) = f(x) which is the definition of an even function

if f(-x) = -f(x) the function is odd... and if neither case occurs the function is neither odd nor even

Answer 2

for a function to be odd:

f(-x) = -f(x)

so lets plug in (-x)

h(-x) = (-x)^2 - (-x)^12
h(-x) = x^2 - x^12 = h(x)

which means h(-x) does not equal -h(x)

For a function to be even:

f(-x) = f(x)

h(-x) = (-x)^2 - (-x)^12
h(-x) = x^2 - x^12
h(-x) = h(x)

yay! the function must be even.

Answer 3

even powers, y intercept 0
even function