Equation: x² + y 2 = 1.Solve the given equation and sketch it after solving.Then determine whether y is a function of x.

Here's the sketch of the circle described by the equation \( x^2 + y^2 = 1 \). The circle is centered at the origin with a radius of 1.

### Key Points:
- The graph is a perfect circle touching points \((1, 0)\), \((-1, 0)\), \((0, 1)\), and \((0, -1)\).
- The equation does not represent \( y \) as a function of \( x \) because for some \( x \) values (like \( x = 0 \)), there are two corresponding \( y \) values.

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### Related Questions:
1. What is the general formula for a circle in 3D space?
2. How do you determine if a curve passes the vertical line test?
3. Can a circle ever represent a function? If so, under what conditions?
4. How would the equation change if the circle were centered at a different point?
5. What other types of conic sections can be analyzed similarly?

#### Tip: When analyzing functions, always check if each \( x \) value corresponds to only one \( y \) value—this is crucial for determining if it’s a function.

Explore how to solve the circle equation x^2 + y^2 = 1 and determine if y is a function of x. This problem involves graphing a circle centered at the origin with a radius of 1, identifying key points on the circle, and using the Vertical Line Test to analyze function behavior. Suitable for high school students.

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