Find the Domain and Range f(x)=x^3-16x

Problem

ƒ(x)=x3−16*x

Solution

1. Identify the type of function. The function ƒ(x)=x3−16*x is a polynomial function.

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

3. State the domain in interval notation. The domain is (−∞,∞)

4. Determine the range. This is an odd-degree polynomial (degree 3) with a positive leading coefficient.

5. Analyze the end behavior. As x→∞ ƒ(x)→∞ and as x→−∞ ƒ(x)→−∞

6. Conclude the range. Since the function is continuous and its limits at infinity cover all values from negative infinity to positive infinity, the range is (−∞,∞)

Final Answer

Domain: *(−∞,∞), Range: *(−∞,∞)

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