To determine the range of the given functions, let’s analyze them one by one:
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y = 2x: This is a linear function. As x approaches negative infinity, y will also approach negative infinity, and as x approaches positive infinity, y will approach positive infinity. Thus, the range of y = 2x is all real numbers.
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y = 25x: Like the previous function, this is also a linear function with the same behavior. Its range is also all real numbers.
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y = 5x2: This is a quadratic function that opens upwards. The smallest value occurs at x = 0, where y = 0. As x moves away from 0 in both directions, y increases without bound. Thus, the range of this function is [0, infinity).
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y = 5x2: This is identical to the previous function and has the same range, which is [0, infinity).
From the analysis, we see that the functions y = 2x and y = 25x have a range of all real numbers, but the functions y = 5x2 (both of them) have a range starting from 0 and extending to infinity. Therefore, if we’re looking for a range that is 2 to infinity, none of these functions specifically meet that criterion, as they either cover more than those bounds or do not fall within the ‘2 to infinity’ range. However, qualitatively, the quadratic functions approach infinity and touch 0 but do not include negative values.