|Module 8 - Continuity|
|Introduction | Lesson 1 | Lesson 2 | Lesson 3 | Self-Test|
|Lesson 8.3: Piecewise Functions|
In this lesson you will modify a piecewise function to make it continuous and then graph the function using Boolean operators.
Consider the function defined by
8.3.1 By using the definition of continuity, find the value of k that makes the function continuous at
Graphing a Piecewise Function
Display the graph of using the value of k that makes the function continuous.
The graph appears to be continuous at x = 2.
8.3.2 Describe how the graph would change if you changed k to 7. Click here for the answer.
Illustrate the result of changing the value of k to 7.
The second part of the piecewise function has been shifted upward, and the function is no longer continuous at x = 2. The discontinuity in this modified function (k = 7) is a jump discontinuity.
8.3.3 Evaluate the left- and right-hand limits of the piecewise function with k = 7 at x = 2. Click here for the answer.
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