Problem preview

F-IF.4 Warmup M1-022-A15-V04

Interpret and sketch key graph/table features in context: intercepts, intervals, maxima/minima, symmetry, end behavior, and periodicity.

Compare graph features with table evidence

Problem

Use the claim-and-table evidence to evaluate the extremum claim. State the evidence verdict, the relevant comparison, what the table establishes, and its limitation.

Evidence card comparing a graph claim of a minimum near 2 comma negative 3 with table values f of 1 equals 1, f of 2 equals negative 3, and f of 3 equals 0.

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verdict = supports an x-intercept at x=2 because f(2) is negative

verdict = contradicts the claim because f(1) and f(3) differ

verdict = proves a global minimum; comparison = -3<1 and 0; limitation = none

verdict = supports a local minimum at sampled x=2; comparisons = -3<1 and -3<0; establishes = f(2) is least among the three tabled values; limitation = these three rows alone do not prove a global minimum over the full domain

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Curriculum context

Course: Math I
Standard: F-IF.4
Category: Functions
Domain: Interpreting Functions
Objective: Interpret and sketch key graph/table features in context: intercepts, intervals, maxima/minima, symmetry, end behavior, and periodicity.
Problem type: Compare graph features with table evidence