Problem preview

F-IF.7.b Warmup M2-022-A13-V02

Graph square-root, cube-root, absolute-value, step, and piecewise-defined functions, showing key features by hand in simple cases and with technology when the functions are more complicated.

Translate a context into an exact piecewise graph record

Problem

Build the runner's total-distance graph \(d\) versus time \(t\). Convert \(6~\text{mph}\) into a distance rule on \(0\le~t\le~1\), preserve the accumulated distance during the rest through \(t=1.5\), and report both segments, their join, domain, range, \(d(0.5)\), and \(d(1.25)\).

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d=6t on [0,1], then d=0 on (1,1.5].

Speed is 6 on [0,1], then 0 on (1,1.5].

d=6t on [0,1], then d=6 on [1,1.5]; segments meet at (1,6); domain [0,1.5]; range [0,6]; d(0.5)=3 miles; d(1.25)=6 miles.

d=6t on [0,1], then d=6(t−1) on (1,1.5].

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Curriculum context

Course: Math II
Standard: F-IF.7.b
Category: Functions
Domain: Interpreting Functions
Objective: Graph square-root, cube-root, absolute-value, step, and piecewise-defined functions.
Problem type: Translate a context into an exact piecewise graph record