Consider the function . The domain of this function is all real numbers. Write the range of this function in interval notation, __________.
Answer & Analysis
Analysis
Question Analysis
This question tests the student's ability to determine the range of a quadratic function. Given that the domain is all real numbers, the range must be determined by analyzing the minimum value of the function.
Key Concept Explanation
For a quadratic function of the form , where a > 0, the parabola opens upwards and has a minimum value at its vertex. The range is from this minimum value to positive infinity.
Step-by-step Solution
1. Identify the given function: .
2. Determine the domain: The domain is all real numbers, .
3. Find the vertex of the parabola: The vertex form is
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