Find the Domain and Range y=x^3

Problem

y=x3

Solution

1. Analyze the domain by identifying any restrictions on the input x Since x3 is a polynomial function, there are no values of x that would result in division by zero or the square root of a negative number.

2. Determine the domain as the set of all real numbers.

D=(−∞,∞)

3. Analyze the range by observing the behavior of the output y As x approaches infinity, x3 approaches infinity. As x approaches negative infinity, x3 approaches negative infinity.

4. Determine the range as the set of all real numbers, since every real number has a unique cube root.

R=(−∞,∞)

Final Answer

Domain: *(−∞,∞), Range: *(−∞,∞)

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