Problem preview

F-IF.7.b Warmup M2-022-A05-V03

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.

Specify piecewise-linear boundaries and continuity

Problem

Graph \(f(x)=-x\) for \(x<2\) and \(f(x)=x-4\) for \(x\ge~2\). Evaluate both formulas at \(x=2\), assign the open and closed boundary points from the inequalities, determine \(f(2)\), and compare the one-sided values to classify continuity.

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Graph y=−x on both sides of x=2, open from the left and closed from the right. The result is one continuous line.

For x≤2, graph y=−x with a closed point at (2,−2). For x>2, graph y=x−3 with an open point at (2,−1). The function has a jump.

For x<2, graph y=−x with an open point at (2,−2). For x≥2, graph y=x−4 with a closed point at (2,−2). The function is continuous.

For x<2, graph y=−x with an open point at (2,−2). For x≥2, graph y=x−3 with a closed point at (2,−1). The function has a jump.

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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: Specify piecewise-linear boundaries and continuity