Question

For these functions, determine which ones are neither even nor odd

a. f(x) = 3x^2 + |x|
b. f(x) = 3x^3 + x^2 +x - 4
c. f(x) = 1/2x
d. f(x) = 2x^5 - x^3 + 2x
e. f(x) = 4x + 1/x
f. f(x) = 2x^4 + x^2 - x + 2

I have to enter each letter but I am soo lost :(

Answer 1

the tests

you need to replace x with -x

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

e.g. f(x) = x^2 then f(-x) = (-x)^2 so f(-x) = x^2 hence f(-x) = f(x)


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

e.g. f(x) = x^3 so f(-x) = (-x)^3 = -x^3 so f(-x) = - f(x)

is its not odd nor even then its neither

eg f(x) = 3x + 1 f(-x) = 3(-x) + 1 = -3x + 1 which is neither f(x) or - f(x)

so its neither.

so substitute -x into each and then check

Answer 2

Nicely explained....

Answer 3

Thank you! :)

Answer 4

Also,the graph of even function is symmetric about y-axis....

Answer 5

and as a hint, (a) is even