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F-IF.9 Warmup M1-027-A14-V04

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

Compare long-term behavior of two functions

Problem

Function \(f\) is described as increasing by \(6\) for every increase of \(1\) in \(x\), with a starting value of \(2\) when \(x=0\). Function \(g\) is given by \(g(x)=x^2\). Compare the long-term behavior of the two functions as \(x\) grows large.

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As x gets very large, f(x)=6x+2 and g(x)=x² grow at the same rate because both increase as x increases.

As x gets very large, f(x)=6x+2 grows faster than g(x)=x² because f increases by 6 every time x increases by 1.

As x gets very large, f(x)=6x+2 stays greater than g(x)=x² because f starts at 2 when x=0.

As x gets very large, g(x)=x² eventually grows faster than f(x)=6x+2 because quadratic growth outpaces linear growth.

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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 long-term behavior of two functions