Problem

Functions \(f\) and \(g\) each have zeros \(-2\) and \(4\), with \(f(0)~=~8\) and \(g(0)~=~-8\). State exactly what the evidence establishes about their matching features and identity, and name the feature categories it does not establish.

Big Picture

What this problem is really about

Separate what the evidence proves from what it leaves unknown. Matching zeros support matching x-intercepts, while one differing output is enough to rule out identical functions. Without rules, domains, or fuller graphs, however, resist extending those facts to range, turning behavior, or end behavior.

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Analysis: Their zeros match, but their y-intercepts differ, so f and g are not the same function. The given facts do not establish other domain, range, turning, or end-behavior features.

Analysis: Their zeros differ, but their y-intercepts differ, so f and g are not the same function. The given facts do not establish other domain, range, turning, or end-behavior features.

Analysis: Their zeros match, but their y-intercepts differ, so f and g are not the same function. The given facts establish other domain, range, turning, or end-behavior features.

Analysis: Their zeros match, but their y-intercepts match, so f and g are not the same function. The given facts do not establish other domain, range, turning, or end-behavior features.

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Functions \(f\) and \(g\) each have zeros \(-2\) and \(4\), with \(f(0)~=~8\) and \(g(0)~=~-8\). State exactly what the evidence establishes about their matching features and identity, and name the feature categories it does not establish.

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