Editing Intermediate value theorem (section)

==Motivation==
[[Image:Intermediatevaluetheorem.svg|thumb|280px|The intermediate value theorem]]

This captures an intuitive property of continuous functions over the [[real number]]s: given ''<math>f</math>'' continuous on <math>[1,2]</math> with the known values <math>f(1) = 3</math> and <math>f(2) = 5</math>, then the graph of <math>y = f(x)</math> must pass through the horizontal line <math>y = 4</math> while <math>x</math> moves from <math>1</math> to <math>2</math>. It represents the idea that the graph of a continuous function on a closed interval can be drawn without lifting a pencil from the paper.