Find the Domain and Range f(x)=(x-3)(x^2-6x-18)

Problem

ƒ(x)=(x−3)*(x2−6*x−18)

Solution

1. Identify the type of function. The expression ƒ(x)=(x−3)*(x2−6*x−18) is a polynomial function.

2. Determine the domain. Since polynomials are defined for all real numbers, there are no restrictions such as division by zero or square roots of negative numbers.

3. State the domain in interval notation.

D=(−∞,∞)

4. Determine the degree of the polynomial. Expanding the expression would result in a leading term of x⋅x2=x3

5. Analyze the range. Because the function is a polynomial of odd degree (degree 3), its end behavior goes to −∞ as x→−∞ and to ∞ as x→∞

6. State the range. Since the function is continuous and covers all values from negative infinity to positive infinity, the range is all real numbers.

R=(−∞,∞)

Final Answer

Domain: *(−∞,∞), Range: *(−∞,∞)

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