1. Continuity and end behavior of functions
3.5 Notes
Continuity and end behavior of functions

2. 3.5 Notes
A function f(x) is continuous on an interval if it is continuous for each value of x in that interval.

3. 3.5 Notes
A function f(x) is continuous at a point (x,y) if it is defined at that point and passes through that point without a break.

4. 3.5 Notes
Not continuous:

5. 3.5 Notes
A function f(x) is continuous at a point (x,y) if it is defined at that point and passes through that point without a break.
A function f(x) is discontinuous if there is a break in the graph at that point.
types of discontinuity:
infinite discontinuity
jump discontinuity
point discontinuity

6. 3.5 Notes
infinite discontinuity:

7. 3.5 Notes
jump discontinuity:

8. 3.5 Notes
point discontinuity:

9. 3.5 Notes
Number your paper 1 – 4. Look at the graph and determine whether the function is continuous or discontinuous. If discontinuous, indicate which type of discontinuity.

10. 3.5 Notes

11. 3.5 Notes Check your answers: 1. discontinuous – point
2. discontinuous – jump
3. continuous
4. discontinuous – infinite

12. 3.5 Notes
Right-end behavior: A function’s right-end behavior is described as being either increasing or decreasing.
There are two ways to determine whether a function is increasing or decreasing:
look at its graph
look at its equation

13. 3.5 Notes
Using the graph:
If the right-end of the function is heading up, then the function is increasing.
If the right-end of the function is heading down, then the function is decreasing.

14. 3.5 Notes Using the graph: Turn to p. 177 in your textbook.
Look at the graphs in problems 13 – 18.
Which are increasing?
15, 16, 17, 18
Which are decreasing?
13, 14

15. 3.5 Notes Using the equation:
If the coefficient of the highest power term is positive, then the function is increasing.
If the coefficient of the highest power term is negative, then the function is decreasing.

16. 3.5 Notes Turn to page to p. 166. 20. increasing 21. decreasing

17. 3.5 Notes Get out your homework from last night.
Look at your graphs for problems 5 – 7.
Determine if the function is continuous or discontinuous. If discontinuous, state the type of discontinuity.
Describe the right-end behavior of the function.