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.

Would you like further details or have any questions?

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.