A continuity is a function that can be drawn as a graph CONTINUOUSLY without anything from stopping it. In simpler terms a continuous graph or function can be drawn without lifting our pencil from the paper because it doesn't have any breaks or jumps in it.
A discontinuity is a break, hole, jump, or whatever in the graph that causes it to be discontinuous. It's easy.
Q2: WHAT IS A LIMIT? WHEN DOES A LIMIT NOT EXIST? WHAT IS THE DIFFERENCE BETWEEN A LIMIT AND A VALUE?
A limit is the intended height of a function. A graph can approach two different directions, left and right. If the height of a function does not reach in the same place from left or right, that is when the limit does not exist. A limit, is the height that a graph needs to reach, and a value is an actual number that a graph reaches. If a graph reaches a hole, that is a limit but it is not a value.
Q3: HOW DO WE EVALUATE LIMITS NUMERICALLY, GRAPHICALLY, AND ALGEBRAICALLY?
Numerically, we can do it on a table with the x value on top, and the limit of the function on the bottom. Graphically, we are just looking at a graph as shown above, and from there we can determine the jumps and discontinuities.Algebraically we use direct substitution and plug in whatever x is approaching.
