Use algebra to determine whether the function 𝑓(𝑥) = 22𝑥3 − 19𝑥 is even, odd, orneither.

Sure, to determine whether the function is even, odd, or neither, we need to apply the definitions of even and odd functions.

An even function is a function for which f(x) = f(-x

Sure, to determine whether the function is even, odd, or neither, we need to apply the definitions of even and odd functions.

An even function is one where f(x) = f(-x) for all x in the domain of the function. An odd function is one where -f(x) = f(-x) for all x in the domain of the function.

Let's first check if the function is even:

f(-x) = 22(-x)^3 - 19(-x) = -22x^3 + 19x

This is not equal to f(x), so the function is not even.

Now let's check if the function is odd:

-f(x) = -(22x^3 - 19x) = -22x^3 + 19x

This is equal to f(-x), so the function is odd.

Therefore, the function 𝑓(𝑥) = 22𝑥^3 − 19𝑥 is odd.