|Module 6 - Continuity|
|Introduction | Lesson 1 | Lesson 2 | Lesson 3 | Self-Test|
|Lesson 6.3: Piecewise Functions|
In this lesson you will modify a piecewise function to make it continuous and then define the function using the with( command.
Suppose the function f(x) is defined by
6.3.1 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 y = f(x) using the value of k that makes the function continuous. Be sure
In the Y= Editor, define y1 as the piecewise function
The graph appears to be continuous at x = 2.
6.3.2 How would the graph change if you changed k to 7? Click here for the answer.
Visualize the result of changing the value of k to 7.
Change the graphing style of y1 from Line to Dot so that the calculator will not connect the two pieces.
The parabolic part 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.
6.3.3 Evaluate the left- and right-hand limits of the piecewise function with k = 7. Click here for the answer.
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