Find the Domain and Range f(x)=x^2

Problem

ƒ(x)=x2

Solution

1. Identify the domain by looking for any values of x that would make the function undefined. Since x2 is a polynomial, it is defined for all real numbers.

2. Express the domain in interval notation.

D=(−∞,∞)

3. Identify the range by analyzing the output values of the function. Since any real number squared is non-negative, x2≥0 for all x

4. Determine the minimum value of the function. The vertex of the parabola is at (0,0) so the smallest possible value for ƒ(x) is 0

5. Express the range in interval notation, including 0 and extending to infinity.

R=[0,∞)

Final Answer

Domain: *(−∞,∞), Range: *[0,∞)

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