Which of the following is the range of the function f(x) = x^2 - 4?

Which of the following is the range of the function f(x) = x^2 - 4?

Correct Answer: [-4, ∞)

Step 1: Identify the function given, which is f(x) = x^2 - 4.
Step 2: Recognize that this is a quadratic function, which typically has a U-shape.
Step 3: Determine the vertex of the quadratic function. The vertex form of a quadratic is f(x) = a(x - h)^2 + k, where (h, k) is the vertex.
Step 4: For f(x) = x^2 - 4, we can see that it can be rewritten as f(x) = 1(x - 0)^2 - 4. Here, the vertex is at (0, -4).
Step 5: Since the parabola opens upwards (the coefficient of x^2 is positive), the minimum value of f(x) occurs at the vertex, which is -4.
Step 6: The function can take any value greater than or equal to -4, so the range starts from -4 and goes to infinity.
Step 7: Write the range in interval notation, which is [-4, ∞).

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