Analyze graph transformations caused by f(x)+k, kf(x), f(kx), and f(x+k); identify even/odd functions.
Classify a function as even, odd, both, or neither
Problem
Classify \(f(x)~=~x^{2}\) as even, odd, both, or neither.
Big Picture
What this problem is really about
The four-way classification comes from testing two identities independently, not from stopping after one fails. We’ll calculate the function at negative x once, then compare that expression with both the original output and its negative. Which identities hold for every x determines whether the function has vertical-axis symmetry, origin symmetry, both, or neither.
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