1. What is continuity? What is discontinuity?
Continuity is when a function is continuous, meaning it can be drawn without lifting your pencil off the page.
Discontinuity is when a function is discontinuous, meaning it has either a hole, a break in the graph, a jump, or if it oscillates.
2. What is a limit? When does a limit exist? 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 that exists anywhere on a graph as long as you reach the same height from both the left and the right.
A limit does not exist if the left hand limit and the right hand limit are not equal.
A limit is the intended height of a function while a value is the actual height of the function.
3. How do we evaluate limits numerically, graphically, and algebraically?
We evaluate limits numerically by making a table that gets really close to the limit but the x-values never actually touch it; graphically by looking at the graph either drawn out or on a calculator and writing out the limits; and algebraically by directly substituting into the function.
