Question
Is it linear non linear a function or not a function:
25 = x^2 + y^2
25 = x^2 + y^2
Answers
GPT-4o mini
The equation \(25 = x^2 + y^2\) represents a circle centered at the origin with a radius of 5.
To analyze whether it's a function:
- A relation is considered a function if, for every input \(x\), there is exactly one output \(y\).
- Rearranging this equation for \(y\) gives us \(y^2 = 25 - x^2\), or \(y = \pm \sqrt{25 - x^2}\).
This shows that for some values of \(x\) (specifically, all values within the interval \([-5, 5]\)), there are two corresponding \(y\) values (one positive and one negative), which means it does not meet the criteria for a function.
Therefore, **the relation defined by the equation \(25 = x^2 + y^2\) is not a function** because not every \(x\) corresponds to a unique \(y\).
Regarding linearity:
- The equation represents a circle, which is a non-linear shape.
Thus, it can be concluded:
- **It is not a function and it is non-linear.**
To analyze whether it's a function:
- A relation is considered a function if, for every input \(x\), there is exactly one output \(y\).
- Rearranging this equation for \(y\) gives us \(y^2 = 25 - x^2\), or \(y = \pm \sqrt{25 - x^2}\).
This shows that for some values of \(x\) (specifically, all values within the interval \([-5, 5]\)), there are two corresponding \(y\) values (one positive and one negative), which means it does not meet the criteria for a function.
Therefore, **the relation defined by the equation \(25 = x^2 + y^2\) is not a function** because not every \(x\) corresponds to a unique \(y\).
Regarding linearity:
- The equation represents a circle, which is a non-linear shape.
Thus, it can be concluded:
- **It is not a function and it is non-linear.**