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 \(f(x)=x+2\) for \(x<1\) and \(f(x)=3\) for \(x\ge~1\). Evaluate both formulas at the boundary \(x=1\), assign the open and closed boundary points from the inequalities, determine \(f(1)\), and compare the one-sided values to classify continuity.
At a piecewise breakpoint, interval ownership and continuity answer different questions. We’ll graph each rule only on its assigned side, use the inequalities to place the open and closed markers, and compare both approached values with the included function value before classifying the connection.
Inside Gozunta
Turn the preview into practice.
More than a preview
Gozunta lets you study this problem—and more than 10,000 others.
Create targeted learning sessions, use hints, check your answer, read the walkthrough, watch the video, print the work, and track your progress.
