Problem preview

F-IF.9 Warmup M2-025-A12-V02

Compare function properties across representations, especially quadratic comparisons.

Choose which function better fits a maximize-or-minimize goal by comparing extrema

Problem

For the goal of reaching at least \(100\) as early as possible, compare \(A(3)=90\), \(A(4)=120\), and \(B(3)=110\). Identify the earliest displayed input where each function is verified to meet the threshold, then base the decision on timing rather than the largest later value.

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Choose A because 120 is greater than 110, so A does a better job reaching the goal.

Choose B because it is already at 110 when the input is 3, so it reaches at least 100 first.

Choose A because it reaches 100 exactly between 3 and 4, while B only shows a value above 100 at 3.

Choose B because its value at input 3 is closer to 100 than A’s value at input 4.

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Curriculum context

Course: Math II
Standard: F-IF.9
Category: Functions
Domain: Interpreting Functions
Objective: Compare function properties across representations, especially quadratic comparisons.
Problem type: Choose which function better fits a maximize-or-minimize goal by comparing extrema