Problem preview

F-IF.7.b Warmup M2-022-A12-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.

Classify step versus piecewise-linear behavior from evidence

Problem

Classify the graph for this situation as step or piecewise-linear: Parking costs $\$3$ for $0<t\le~1~\text{hour}$ and $\$2$ more for each additional started hour.

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Piecewise-linear function through (0,3), (1,3), and (2,5).

Piecewise-linear function with slope 3 on 0<t≤1 and slope 2 after t=1.

Step function: C(t)=3 for 0<t≤1 and C(t)=5 for 1<t≤2, increasing by $2 for each additional started hour.

Linear function C(t)=3t+2 for t>0.

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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: Classify step versus piecewise-linear behavior from evidence

Classify the graph for this situation as step or piecewise-linear: Parking costs \(\$3\) for \(0<t\le~1~\text{hour}\) and \(\$2\) more for each additional started hour.

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