Find the Domain and Range f(x)=x^3

Problem

ƒ(x)=x3

Solution

1. Identify the type of function. The function ƒ(x)=x3 is a polynomial function (specifically a cubic function).

2. Determine the domain. Polynomial functions are defined for all real numbers because there are no denominators that could be zero and no even-indexed roots of negative numbers.

3. Express the domain in interval notation. Since x can be any real value, the domain is (−∞,∞)

4. Determine the range. As x approaches infinity, x3 approaches infinity. As x approaches negative infinity, x3 approaches negative infinity.

5. Analyze the continuity. Because the function is continuous and covers all values from negative infinity to positive infinity, the range is all real numbers.

6. Express the range in interval notation. The range is (−∞,∞)

Final Answer

Domain: *(−∞,∞), Range: *(−∞,∞)

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