Analyze graph transformations caused by f(x)+k, kf(x), f(kx), and f(x+k); identify even/odd functions.
Determine whether a function is odd
Problem
Determine whether \(f(x)=3x\) is odd.
Big Picture
What this problem is really about
Oddness requires more than getting different outputs at opposite inputs: the outputs must be exact opposites for every x. We’ll compute the function at negative x, separately negate the original function value, and compare the two simplified expressions. Matching expressions establish the rotational symmetry condition about the origin.
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