One Point Is Not an Interval

You'll learnthat continuous on an interval means continuous at every point of it, how to check that without testing every point, and why a closed endpoint is checked from inside only.

The shaded band is the interval the claim is about. A test that passes at one input inside it says nothing about the rest, so the real method names the function's family and checks the few places it can fail. At the two ends only one side is inside the band, and that is the side you check. Twelve short steps; press Next for each one.

12 STEPS · 6 QUICK CHECKS · EVERY POINT · THE ENDS FROM INSIDE · v2

continuous on the band means at every point of it, and a closed end is checked from inside

Before you start

What you're looking at

One graph with a shaded band across the inputs from 1 to 5. The band is the interval the claim is about; everything outside it is not part of the question.

The question

Is the function continuous at every single input inside the band?

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