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The given function is \( f(x) = x^2 - 2 \) with a specified domain \( \{0, 4, 5, 7, 8\} \). We are tasked with finding the range of this function.

### Step-by-step process:

1. **Evaluate the function for each value in the domain:**
   - For \( x = 0 \): 
     \[
     f(0) = 0^2 - 2 = -2
     \]
   - For \( x = 4 \): 
     \[
     f(4) = 4^2 - 2 = 16 - 2 = 14
     \]
   - For \( x = 5 \): 
     \[
     f(5) = 5^2 - 2 = 25 - 2 = 23
     \]
   - For \( x = 7 \): 
     \[
     f(7) = 7^2 - 2 = 49 - 2 = 47
     \]
   - For \( x = 8 \): 
     \[
     f(8) = 8^2 - 2 = 64 - 2 = 62
     \]

2. **List the outputs (range values):**
   The range is the set of all the output values, which are:
   \[
   \{-2, 14, 23, 47, 62\}
   \]

### Conclusion:
The range of the function \( f(x) = x^2 - 2 \) with the domain \( \{0, 4, 5, 7, 8\} \) is \( \{-2, 14, 23, 47, 62\} \).

Would you like further details or clarifications?

Here are some additional questions you might find useful:
1. What happens to the range if the domain includes negative numbers?
2. How does the range of a quadratic function generally behave?
3. What would the range be if the domain were all real numbers?
4. How would the function change if we added a constant to it?
5. What effect does squaring a number have on the range of the function?

**Tip:** When dealing with quadratic functions, always consider that their outputs are symmetric about their vertex, and that this symmetry affects the range.

f(x) = x^2 - 2 with domain {0, 4, 5, 7, 8}. Find the range.

Discover how to find the range of the quadratic function f(x) = x^2 - 2 with the domain {0, 4, 5, 7, 8}. This detailed solution is designed for students in Grades 9-11 and covers important algebraic concepts.

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