Problem

Given that \(f\) has a global maximum of \(50\), use the graph evidence at \(x_{0}\) to state the bound on \(f\), compare \(g(x_{0})\) and \(f(x_{0})\), and limit the conclusion to the scope the evidence proves.

Clean source evidence without the requested comparison conclusion.

Answer choices

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Preview only

bound = f(x)≤50 for every modeled x; evidence = g(x₀)>50; conclusion at x₀ = g(x₀)>f(x₀); scope = g>f for every modeled input merely because g eventually exceeds 50

bound = f(x)≤50 for every modeled x; evidence = g(x₀)>50; conclusion at x₀ = f(x₀)>g(x₀) because f has a maximum; scope = f exceeds g wherever g>50

bound = f(x)≤50 for every modeled x; evidence = g(x₀)>50; conclusion at x₀ = g(x₀)>50≥f(x₀), so g(x₀)>f(x₀); scope = proved wherever graph establishes g>50, not necessarily at earlier inputs

bound = f(x)≤50 for every modeled x; evidence = g(x₀)>50; conclusion at x₀ = evidence is insufficient without an exact listed value; scope = no comparison can be made anywhere

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Given that \(f\) has a global maximum of \(50\), use the graph evidence at \(x_{0}\) to state the bound on \(f\), compare \(g(x_{0})\) and \(f(x_{0})\), and limit the conclusion to the scope the evidence proves.

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