Analyze graph transformations across radical, rational, exponential, logarithmic, and other functions; recognize even and odd functions.
Classify a function as even, odd, both, or neither
Problem
Is \(f(x)=0\) even, odd, both, or neither?
Big Picture
What this problem is really about
Even and odd are separate definition tests, not automatically exclusive labels. After confirming domain symmetry, compare f of negative x first with f of x and then independently with negative f of x. For a special constant output, pay close attention to whether taking its additive inverse actually changes the value; the classification follows every definition that holds.
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