# Determine if the following function is even, odd, or neither: f(x) = -9x^{4} + 5x + 3

An even function is always symmetric about the y-axis, while an odd function is symmetric about the origin.

## Answer: f(x) is clearly neither equal to f(-x) nor equal to -f(-x), so it is neither odd nor even function.

Go through the step by step process to understand the derivability of the nature of the function.

**Explanation:**

Given expression: f(x) = -9x^{4} + 5x + 3

__Condition of even and odd functions:__

1) For odd functions -

f(x) = -f(-x)

2) For even functions.

f(x) = f(-x)

3) If none of the above conditions hold true, then the function is neither odd nor even.

Let's check for the expression, f(x) = -9x^{4} + 5x + 3

Replace x by -x

f(-x) = 9(-x)^{4} + 5(-x) + 3

⇒ f(-x) = 9x^{4} - 5x + 3

Also we can see the value of -f(-x),

⇒ -f(-x) = -9x^{4} + 5x - 3

We can conclude that f(x) ≠ f(x) ≠ -f(-x)