Find the Domain and Range f(x)=x^2+3

Problem

ƒ(x)=x2+3

Solution

1. Identify the type of function. The function ƒ(x)=x2+3 is a polynomial (specifically a quadratic function).

2. Determine the domain. Since there are no denominators containing variables and no square roots of negative numbers, 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 + 3 = 3$.

5. Conclude the range. Because the parabola opens upward, the function takes all values from 3 to infinity.

Final Answer

Domain: *(−∞,∞), Range: *[3,∞)

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