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
To determine if a function is even or odd, we need to check if it satisfies the even or odd property for all x.
A function is even if f(x) = f(-x) for all x in the domain.
Let's check if f(x) = f(-x) for our function f(x) = x^3 - 2x + 3.
f(-x) = (-x)^3 - 2(-x) + 3
= -x^3 + 2x + 3
Since f(-x) = -x^3 + 2x + 3 is not equal to f(x) = x^3 - 2x + 3, we can conclude that the function is not even.
A function is odd if f(x) = -f(-x) for all x in the domain.
Let's check if f(x) = -f(-x) for our function f(x) = x^3 - 2x + 3.
-f(-x) = -(-x)^3 + 2(-x) + 3
= -(-x^3) - 2x + 3
= x^3 + 2x + 3
Since f(x) = x^3 - 2x + 3 is not equal to -f(-x) = x^3 + 2x + 3, we can conclude that the function is not odd.
Therefore, the function f(x) = x^3 - 2x + 3 is neither even nor odd.