Compare function properties across representations, especially quadratic comparisons.
Compare two function values at the same input across representations
Problem
Compare \(A(x)=x^{2}+1\) and \(B(x)=3x\) at the common input \(x=2\). Substitute \(2\) into each complete expression, show \(A(2)\) and \(B(2)\), and use the resulting outputs to state the greater value.
Big Picture
What this problem is really about
A pointwise comparison is fair only when both functions use the same allowable input. We’ll verify domain membership, evaluate each complete representation at that input, and compare the outputs and their signed difference rather than comparing coefficients.
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