Compare two functions represented in different ways: equations, graphs, tables, or verbal descriptions.
Compare long-term behavior of two functions
Problem
Compare the long-term behavior of \(f(x)=10x\) and \(g(x)=2^x\).
Big Picture
What this problem is really about
Long-term behavior cannot be decided by comparing one early pair of outputs or the visible constants alone. We’ll contrast a fixed amount added per step with a fixed factor applied per step, then examine values at increasingly large inputs. The repeated-change structures, rather than a temporary lead, explain which trend ultimately controls the comparison.
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