Question

Using interval (-8,8) construct 3 graphs using the given interval. Prove that it is continuous.

Answer 1

Answer:

Many functions have the property that their graphs can be traced with a pencil without lifting the pencil from the page. Normally, such functions are called continuous. Other functions have points at which a break in the graph occurs, but satisfy this property over intervals contained in their domains. They are continuous on these intervals and are said to have a discontinuity at a point where a break occurs.

We begin our investigation of continuity by exploring what it means for a function to have continuity at a point. Intuitively, a function is continuous at a particular point if there is no break in its graph at that point.