1. Continuity and End Behavior
Section 3-5

2. I can determine whether a function is continuous or discontinuous
Learning Target
I can determine whether a function is continuous or discontinuous
I can identify the end behavior of functions
I can determine whether a function is increasing or decreasing on an interval

3. The chart below shows the different types of discontinuous functions.
Continuous Function-the graph of this function is smooth or continuous curves. (Linear and Quadratic Function)
Discontinuous function- the graph of this function cannot be trace without lifting your pencil (step wise and absolute value).
The chart below shows the different types of discontinuous functions.
Function
Name
Graph
Characteristics
Infinite
Discontinuity
The graph becomes greater and greater as it approaches a given x-value.

4. Jump Discontinuity Point Function Name Graph Characteristics
Jump
Discontinuity
The graph stops at a given value of the domain and then begins again at a different range value for the same value of the domain.
Point
When there is a value in the domain for which the function is undefined, but the pieces of the graph match up. There is a hole in the graph.

5. Continuity Test
A function is continuous at x = c if it satisfies the following conditions:
1. the function is defined at c; or f(c) exists
2. the function approaches the same y-value on the left and right sides of x = c
3. the y-value that the function approaches from each side is f(c).

6. Example: Determine whether the function is continuous at the
given x-value.

12. Another characteristic of functions used for analysis is the monotonicity of the function. This means that on an interval, the function is increasing or decreasing on that particular interval. Whether a graph is increasing or decreasing is always judged by viewing a graph from left to right.

18. Helpful Websites Discontinuity:
End behavior:
3-5 Self Check Quiz: