3.5 Notes

Continuity and end behavior of functions

3.5 Notes

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

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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.

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Not continuous:

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

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infinite discontinuity:

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jump discontinuity:

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point discontinuity:

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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.

1. 2.

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3. 4.

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Check your answers:

1. discontinuous – point

2. discontinuous – jump

3. continuous

4. discontinuous – infinite

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• 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

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.

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

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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.

3.5 Notes

• Turn to page to p. 166.

20. increasing

21. decreasing

22. increasing

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• 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.