My Learning Cart
?
Categories
Account

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

₹0.0
Login to Download
  • 📥 Instant PDF Download
  • ♾ Lifetime Access
  • 🛡 Secure & Original Content

What’s inside this PDF?

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

Options:

  1. (-∞, -4]
  2. [-4, ∞)
  3. (-4, ∞)
  4. [0, ∞)

Correct Answer: [-4, ∞)

Solution: 

The minimum value of f(x) is -4 when x=0, so the range is [-4, ∞).

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

Practice Questions

Q1
Which of the following is the range of the function f(x) = x^2 - 4?
  1. (-∞, -4]
  2. [-4, ∞)
  3. (-4, ∞)
  4. [0, ∞)

Questions & Step-by-Step Solutions

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, ∞).
No concepts available.
Soulshift Feedback ×

On a scale of 0–10, how likely are you to recommend The Soulshift Academy?

Not likely Very likely
Home Practice Performance eBooks