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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?
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Practice Questions
1 question
Q1
Which of the following is the range of the function f(x) = x^2 - 4?
(-∞, -4]
[-4, ∞)
(-4, ∞)
[0, ∞)
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The minimum value of f(x) is -4 when x=0, so the range is [-4, ∞).
Questions & Step-by-step Solutions
1 item
Q
Q: Which of the following is the range of the function f(x) = x^2 - 4?
Solution:
The minimum value of f(x) is -4 when x=0, so the range is [-4, ∞).
Steps: 7
Show Steps
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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