Check whether the following represent function or not
`x^(2)+y^(2)=36, xepsilon[-6,6]`

Explanation

To determine whether the equation \( x^2 + y^2 = 36 \) represents a function, we need to analyze the relationship between \( x \) and \( y \).

### Step-by-Step Solution:

1. **Identify the Equation**: The given equation is \( x^2 + y^2 = 36 \). This is the equation of a circle centered at the origin (0,0) with a radius of 6.

2. **Rewrite the Equation**: We can rewrite the equation in terms of \( y \):
\[ y^2 = 36 - x^2 \]
Taking the square root of both sides gives:
\[ y = \pm \sqrt{36 - x^2} \]

3. **Analyze the Values of \( y \)**: For each value of \( x \) within the interval \([-6, 6]\), we need to check how many values of \( y \) correspond to it. The expression \( \sqrt{36 - x^2} \) will yield two values for \( y \) (one positive and one negative) for any \( x \) in the interval except at the points where \( x = -6 \) and \( x = 6 \), where \( y = 0 \).

4. **Example Calculation**: Let’s take a specific value of \( x \), say \( x = 3 \):
\[ y^2 = 36 - 3^2 = 36 - 9 = 27 \]
Thus,
\[ y = \pm \sqrt{27} = \pm 3\sqrt{3} \]
This means for \( x = 3 \), there are two corresponding values of \( y \): \( 3\sqrt{3} \) and \( -3\sqrt{3} \).

5. **Conclusion**: Since a function is defined as a relation where each input (value of \( x \)) corresponds to exactly one output (value of \( y \)), and we have found that for \( x = 3 \) there are two outputs, we conclude that the relation does not represent a function.

### Final Answer:
The equation \( x^2 + y^2 = 36 \) does not represent a function.

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