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Determina se la seguente funzione sono relative a X o meno. In caso affermativo affermane il dominio e descrivile 

The given graph shows a semicircle centered at the origin with a radius of 1. This type of graph corresponds to the equation of a circle.

For a circle centered at the origin \((0, 0)\) with radius \( r \), the equation is:
\[ x^2 + y^2 = r^2 \]

Given the graph, the radius \( r = 1 \), thus the equation of the full circle is:
\[ x^2 + y^2 = 1 \]

Since the graph shows only the upper semicircle, we need to consider only the positive values of \( y \). Therefore, the equation representing the upper semicircle is:
\[ y = \sqrt{1 - x^2} \]

### Determining the Domain
The domain of this function includes all \( x \) values for which the expression under the square root is non-negative:
\[ 1 - x^2 \geq 0 \]
\[ x^2 \leq 1 \]
\[ -1 \leq x \leq 1 \]

Thus, the domain of the function \( y = \sqrt{1 - x^2} \) is:
\[ [-1, 1] \]

### Summary
- The function \( y = \sqrt{1 - x^2} \) describes the upper semicircle.
- The domain of this function is \( [-1, 1] \).

Would you like more details or have any questions?

Here are some related questions you might find interesting:
1. What is the range of the function \( y = \sqrt{1 - x^2} \)?
2. How would the graph change if the equation were \( y = -\sqrt{1 - x^2} \)?
3. What is the area of the semicircle described by \( y = \sqrt{1 - x^2} \)?
4. How do you derive the equation of a circle from its geometric properties?
5. What would be the equation and graph of a semicircle centered at \((h, k)\) with radius \( r \)?

### Tip
When analyzing functions, always start by identifying their type, which helps in determining their key properties such as domain, range, and behavior.

Determina se la seguente funzione sono relative a X o meno. In caso affermativo affermane il dominio e descrivile

Discover the properties of a semicircle on the coordinate plane, centered at the origin with radius 1. This guide provides the equation y = sqrt(1 - x^2) and the domain [-1, 1], suitable for high school level students.

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