Equation: x² + y 2 = 1.
Solve the given equation using the “assumption method” let x = ___.  Sketch it after solving.Then determine whether y is a function of x.

Here is the graph based on the assumption method, along with the full circle for context. The red points represent the specific values we assumed for \( x \) and their corresponding \( y \) values.

### Step 3: Determine if \( y \) is a Function of \( x \)

As we observed earlier, for most values of \( x \), there are multiple \( y \) values (one positive and one negative). This violates the requirement for a function, where each \( x \) value should correspond to exactly one \( y \) value. Therefore, **\( y \) is not a function of \( x \)**.

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### Related Questions:
1. What happens if we assume negative values of \( x \)? How does it affect \( y \)?
2. How would the solution change if we assumed non-integer values for \( x \)?
3. Can the assumption method be applied to non-circular equations?
4. What is the range of \( y \) for all possible \( x \) values in this equation?
5. How does this assumption method help in understanding the shape of the graph?

#### Tip: The assumption method is a useful way to explore the behavior of an equation by testing specific values, especially when learning about the graph's shape and properties.

Explore the solution to the equation x² + y² = 1 using the assumption method and determine if y is a function of x. This detailed analysis includes graphing techniques and insights into the behavior of the equation. Suitable for high school students studying advanced algebra and graphing functions.

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