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If the domain of a piecewise-defined function f is all real numbers, must the range of f also be all real numbers?

User Joel Shea
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Final answer:

Yes, if the domain of a piecewise-defined function f is all real numbers, then the range of f must also be all real numbers.

Step-by-step explanation:

Yes, if the domain of a piecewise-defined function f is all real numbers, then the range of f must also be all real numbers.

A piecewise-defined function is a function that is defined by different rules on different parts of its domain.

In this case, we are told that f is a horizontal line for 0 ≤ x ≤ 20, which means that the value of f is constant within that interval.

Since the domain of f is all real numbers, there are no restrictions on the possible values of x.

Therefore, the range of f will also be all real numbers, as the value of f can be any real number.

User Brad At Kademi
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