Problem preview

F-IF.9 Warmup M1-027-A10-V04

Compare two functions represented in different ways: equations, graphs, tables, or verbal descriptions.

Compare which function is greater over an interval

Problem

Use the displayed table to compare \(f\) and \(g\) at every listed input in \([0,~2]\). State each comparison with its numerical evidence.

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g is greater on the interval because g starts greater at x = 0, so there is no need to check x = 1 and x = 2.

At x = 0, 1, and 2, g is greater than f because 6 > 4, 8 > 5, and 10 > 7.

At x = 0, 1, and 2, f is greater than g because f increases from 4 to 7 across the interval.

At x = 0 and 1, g is greater, but at x = 2 the functions are equal because 10 and 7 are both close to 8.

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Curriculum context

Course: Math I
Standard: F-IF.9
Category: Functions
Domain: Interpreting Functions
Objective: Compare two functions represented in different ways: equations, graphs, tables, or verbal descriptions.
Problem type: Compare which function is greater over an interval