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

Problem

ƒ(x)=x2+2

Solution

1. Identify the type of function. The function ƒ(x)=x2+2 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 range by looking at the vertex. The term x2 is always greater than or equal to 0 for any real x

4. Calculate the minimum value. Since the minimum value of x2 is 0 the minimum value of ƒ(x) is 0 + 2 = 2$.

5. Conclude the range. The function values start at 2 and increase toward infinity as x moves away from 0

Final Answer

Domain: *(−∞,∞), Range: *[2,∞)

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