U2-L6 Piecewise Function

​Piecewise Function

Is a function defined by two or more equations. Each “piece”

of the function applies to a different part of its domain.

Essential Understandings

1.Piecewise-defined functions are often discontinuous.

​

2.One-sided Limits: To find the limit from the right we must use the rule that has a greater than  symbol. To find the limit from the left  we must use the rule that has a than  symbol.

​

3. Two-sided Limits: To find the limit we must first find the limits from the left and from the right.

​Learning Target

To use an algebraic method to determine Piecewise Functions by using the properties of limits?

​Example 1

To find the limit from the right we must use the rule that has a greater than  symbol. To find the limit from the left  we must use the rule that has a than  symbol.​

​Steps

1. Determine the side of which the limit is approaching.​

2. Choice the piece wise function that is associated.

3. Find the limit of x​ value it is approaching.

​Solution

​Write down any questions on your paper.

​

​Example 2

Two-sided Limits: To find the limit we must first find the limits from the left and from the right.

​Steps

1. FinD the limit of both functions.​

2. Determine if the limit exist.

3. If the limit exist state the limit if it doesn't state why the limit does not exist.

​Solution

​Write down any questions on your paper.

​

Multiple Choice

Does this limit exist? If so what is limit?

• DNE

• 2

• 10

• 4

Multiple Choice

Does this limit exist? If so what is limit?

• DNE

• -5

• -1

• 5