Find the Domain and Range f(x)=x^2+4

Problem

ƒ(x)=x^2+4

Solution

1. Identify the type of function. The expression x^2+4 is a polynomial (specifically a quadratic function).

2. Determine the domain. Since there are no denominators containing x and no square roots of negative values to avoid, the function is defined for all real numbers.

3. Analyze the range by looking at the vertex. The term x^2 is always greater than or equal to 0 for any real x

4. Calculate the minimum value. Adding 4 to both sides of the inequality x^2≥0 gives x^2+4≥4

5. Conclude the range. The output values ƒ(x) start at 4 and increase to infinity.

Final Answer

Domain: *(−∞,∞), Range: *[4,∞)

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