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 even
Problem
Determine whether \(f(x)=x^{2}+3\) is even.
Big Picture
What this problem is really about
Evenness is a statement about every pair of opposite inputs, so a few numerical checks are not enough. We’ll substitute negative x into the rule, simplify carefully, and compare the result with the original function. Equality for every x is the algebraic version of symmetry across the vertical axis.
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