Determine whether the function is even, odd, or neither.
f(x)=-4x²+5x
Its odd right?
neither.
To determine whether the function is even, odd, or neither, we need to check if it satisfies certain conditions.
A function is defined as even if f(-x) = f(x) for all x in the domain of the function. In other words, if replacing x with -x in the function gives the same expression, then the function is even.
A function is defined as odd if f(-x) = -f(x) for all x in the domain of the function. In other words, if replacing x with -x in the function gives the negative of the expression, then the function is odd.
Let's apply these conditions to the function f(x) = -4x² + 5x:
1. Check for evenness:
f(-x) = -4(-x)² + 5(-x)
= -4x² - 5x
f(x) = -4x² + 5x
Comparing f(-x) and f(x), we can see that these expressions are not equal. Therefore, the function is not even.
2. Check for oddness:
f(-x) = -4(-x)² + 5(-x)
= -4x² - 5x
-f(x) = -(-4x² + 5x)
= 4x² - 5x
Comparing f(-x) and -f(x), we can see that these expressions are not equal. Therefore, the function is not odd.
Since the function does not satisfy either condition, it is neither even nor odd.
In conclusion, the function f(x) = -4x² + 5x is neither even nor odd.