State the domain and range of g.
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.
Is g continuous at x = 2? Explain.
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.
Is g continuous for all values of x?
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?
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Click the link at right for the full version of the eTool: Calc 1-24 HW eTool