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Click on the circles next to each equation in the eTool below to view it.
Click the link at right for the full version of the eTool: Calc 1-24 HW eTool

Consider the domain and range of each piece separately . Then combine.
Domain: Both 2x and 3x − 2 have a domain of all real numbers.
Range: 2x on x ≤ 2 has a range of 0 < y ≤ 4 and 3x − 2 on x > 2 has a range of 4 < y.

Later in this course we will learn a formal definition of continuity. For now, think about what continuous means to you. Now look at the graph at x = 2. Make a conclusion and justify.

Consider other values of x, other than x = 2. Is the function continuous at these point? Is there anywhere where the function will not be continuous?