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What is the range of

A piecewise function g of x, where part 1 is x squared minus 5 for x less than 2 and part 2 is 2 times x for x greater than or equal to 2.?

User Halmon
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The range of a function refers to the set of all possible output values. To find the range of the given piecewise function g(x), we need to consider the two cases separately:

Case 1: x < 2

In this case, g(x) = x^2 - 5. The graph of this function is a parabola that opens upward and has a vertex at (0,-5). Since the parabola is open upward, the minimum value of g(x) occurs at the vertex and is g(0) = -5. As x increases, g(x) increases without bound. Therefore, the range of g(x) for x < 2 is (-5, ∞).

Case 2: x ≥ 2

In this case, g(x) = 2x. The graph of this function is a line with slope 2 and y-intercept 0. Since the line has a positive slope, g(x) increases as x increases. Therefore, the range of g(x) for x ≥ 2 is [4, ∞).

To find the overall range of g(x), we need to consider the union of the two ranges, which is (-5, ∞).

User Norbert Lange
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