Find the Domain and Range f(x)=x^2-1

Problem

ƒ(x)=x2−1

Solution

1. Identify the type of function. The function ƒ(x)=x2−1 is a polynomial (specifically a quadratic function).

2. Determine the domain. Since there are no square roots of negative numbers or divisions by zero, the function is defined for all real numbers.

3. Analyze the vertex to find the range. The graph is a parabola that opens upward because the coefficient of x2 is positive.

4. Calculate the ycoordinate of the vertex. The minimum value occurs at x=0

5. Evaluate ƒ(0) to find the minimum yvalue.

ƒ(0)=0−1

ƒ(0)=−1

6. Conclude the range. Since the minimum value is −1 and the parabola opens upward, the range includes all values greater than or equal to −1

Final Answer

Domain: *(−∞,∞), Range: *[−1,∞)

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