In the right hand diagram a blue disc is displayed. This represents an open set \(B\) in the codomain. The blue shape in the left hand diagram is the inverse image of this set.

In the left hand diagram there is a yellow disc with a red dot at the centre. The red dot represents a point \(z\) in the inverse image of \(B\) and the yellow disc represents the open ball \(B(z,\delta)\). The yellow shape in the right hand diagram is the image of \(B(z,\delta)\) under the current function. For a continuous function it is possible to reduce \(\delta\) so that \(B(z,\delta)\) is completely within the inverse image of \(B\) - and hence the right hand yellow shape completely with \(B\).

The fifth function is not continuous and \(z\) has been chosen to show that it is not possible to reduce \(\delta\) so that \(B(z,\delta)\) is completely within the inverse image of \(B\) - and hence the right hand yellow shape completely with \(B\).

• Zoom in or out, by pressing the appropriate buttons.
• Use the slider (or in older browsers) the drop down list to reduce the value of \(\delta\) by the chosen factor.
• Press 'Reset' to return to the initial state.
• Choose the function from the list.