Slide to connect

Build the Bridge

A function is continuous if limits from both sides match the value. Find the value of k to make continuous at .

x y
Drag to patch

Fix the Hole

A removable discontinuity (a hole) can be fixed by defining a single point. Drag the patch to fix the removable discontinuity!

Magic Point Patch

Draw continuous path

The IVT River

Draw a continuous curve from A to B. Can you do it without crossing the river ()? (Hint: The Intermediate Value Theorem says no!)

y = 0 (River) IVT Crossing! A B
Draw here
Tap to scan

Find the Root

IVT guarantees a root () exists between and if their signs are opposite.

Tap the x-values below to scan their signs and find the interval containing the root!

Root in ({{ s4_foundInterval[0] }}, {{ s4_foundInterval[1] }}) {{ xVal }} {{ s4_calcY(xVal) > 0 ? '+' : '−' }} ?

Master of Continuity!

You've successfully built bridges, patched holes, navigated the IVT river, and found hidden roots. The mathematical world is continuous once again!