Determine whether the following function are even/odd/neither even nor odd?
`f:[-2,3]to[0,9],f(x)=x^(2)`

Explanation

To determine whether the function \( f(x) = x^2 \) defined from the interval \([-2, 3]\) to \([0, 9]\) is even, odd, or neither, we will follow these steps:

### Step 1: Understand the definitions of even and odd functions
- A function \( f(x) \) is **even** if \( f(-x) = f(x) \) for all \( x \) in the domain.
- A function \( f(x) \) is **odd** if \( f(-x) = -f(x) \) for all \( x \) in the domain.

### Step 2: Check if the function is even
To check if \( f(x) \) is even, we need to evaluate \( f(-x) \) and compare it with \( f(x) \).

1. Calculate \( f(-x) \):
\[ f(-x) = (-x)^2 = x^2 = f(x) \]

2. Since \( f(-x) = f(x) \) for all \( x \) in the domain \([-2, 3]\), we conclude that the function is even.

### Step 3: Check if the function is odd
To check if \( f(x) \) is odd, we need to evaluate \( f(-x) \) and compare it with \(-f(x)\).

1. We already calculated \( f(-x) \):
\[ f(-x) = x^2 \]

2. Calculate \(-f(x)\):
\[ -f(x) = -x^2 \]

3. Since \( f(-x) = x^2 \) is not equal to \(-f(x) = -x^2\) for any \( x \) in the domain, we conclude that the function is not odd.

### Final Conclusion
Since the function \( f(x) = x^2 \) satisfies the condition for being even but does not satisfy the condition for being odd, we conclude that:

**The function is even.**

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