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The problem asks to find the range of the function \( f(x) = x^2 - 2x - 7 \) given the domain \( \{-5, -1, 4\} \).

To find the range, we'll evaluate the function for each value in the domain.

1. **For \( x = -5 \):**
   \[
   f(-5) = (-5)^2 - 2(-5) - 7 = 25 + 10 - 7 = 28
   \]

2. **For \( x = -1 \):**
   \[
   f(-1) = (-1)^2 - 2(-1) - 7 = 1 + 2 - 7 = -4
   \]

3. **For \( x = 4 \):**
   \[
   f(4) = (4)^2 - 2(4) - 7 = 16 - 8 - 7 = 1
   \]

Thus, the range of the function for the domain \( \{-5, -1, 4\} \) is \( \{28, -4, 1\} \).

The correct answer is **A: \{-4, 1, 28\}**.

Would you like further details on any of the calculations?

Here are five related questions to deepen your understanding:
1. How would the range change if the domain were extended?
2. What is the vertex of the parabola \( f(x) = x^2 - 2x - 7 \)?
3. How would you determine the range for an arbitrary quadratic function?
4. What role does the axis of symmetry play in the range of a quadratic function?
5. How can you find the minimum or maximum value of a quadratic function using derivatives?

**Tip:** When working with quadratic functions, identifying the vertex can help you quickly determine the range when the domain includes all real numbers.

Find the range of the function f(x) = x^2 - 2x - 7 given a domain of {-5, -1, 4}.

Learn how to find the range of the quadratic function f(x) = x^2 - 2x - 7 for a given domain of {-5, -1, 4}. This detailed solution includes step-by-step evaluation of the function for each domain value. Suitable for students in Grades 9-10.

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