https://file.aiquickdraw.com/mathbot/file/1732216392542ipdljkiv.jpg

Determine whether each of the following functions is even, odd, or neither.

from PIL import Image
import pytesseract

# Open the image file
image_path = "/mnt/data/1732216392542ipdljkiv.jpg"
image = Image.open(image_path)

# Use OCR to extract text from the image
extracted_text = pytesseract.image_to_string(image)
extracted_text'b) g(a) = a3 -2\n''b) g(a) = a3 -2\n'successThe given function is \( g(x) = x^3 - 2 \). Let us determine whether it is even, odd, or neither.

### Steps:
1. **Check if the function is even**: A function is even if \( g(-x) = g(x) \) for all \( x \).
   - Substitute \( -x \) into \( g(x) \):  
     \( g(-x) = (-x)^3 - 2 = -x^3 - 2 \).  
     Clearly, \( g(-x) \neq g(x) \), so the function is **not even**.

2. **Check if the function is odd**: A function is odd if \( g(-x) = -g(x) \) for all \( x \).
   - Substitute \( -x \) into \( g(x) \):  
     \( g(-x) = -x^3 - 2 \).  
     \( -g(x) = -(x^3 - 2) = -x^3 + 2 \).  
     Clearly, \( g(-x) \neq -g(x) \), so the function is **not odd**.

3. **Conclusion**: Since \( g(x) \) is neither even nor odd, the function is classified as **neither**.

Would you like more examples or further clarification?

### Related Questions:
1. What are the conditions for a function to be classified as even or odd?
2. Can you give another example of a function that is neither even nor odd?
3. How do transformations (like adding/subtracting constants) affect the symmetry of functions?
4. What is the graphical interpretation of even and odd functions?
5. Are there cases where a function can be both even and odd?

**Tip**: To quickly verify symmetry properties, compare \( g(-x) \), \( g(x) \), and \( -g(x) \) side-by-side.

Analyze the function g(x) = x^3 - 2 to determine whether it is even, odd, or neither. Learn about the definitions of symmetry in functions with step-by-step explanations, suitable for high school students.

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