Algebraically, determine whether the following function is even, odd, or neither. Make sure to include your work for full credit. f(x)=x3−2x+3 (1 point) Responses Neither Neither Even Even Odd
To determine if a function is even, odd, or neither, we need to analyze its algebraic expression.
For an even function, we have f(x) = f(-x) for all x in the domain of the function.
For an odd function, we have f(x) = -f(-x) for all x in the domain of the function.
Let's check if the given function, f(x) = x^3 - 2x + 3, satisfies either of these criteria.
1. f(x) = f(-x):
Substituting -x for x in the function, we get f(-x) = (-x)^3 - 2(-x) + 3 = -x^3 + 2x + 3
Since -x^3 + 2x + 3 is not equal to x^3 - 2x + 3, the function does not satisfy the condition for an even function.
2. f(x) = -f(-x):
Substituting -x for x in the function, we get -f(-x) = -(-x)^3 + 2(-x) + 3 = x^3 + 2x + 3
Since x^3 + 2x + 3 is also not equal to x^3 - 2x + 3, the function does not satisfy the condition for an odd function.
Therefore, the given function f(x) = x^3 - 2x + 3 is neither even nor odd.