is y2=6-x2 a function

If you meant

y^2 = 6 - x^2, then it is NOT a function

(For each x I choose , I do not get a unique value of y
your equation represents a circle)

To determine if the equation y^2 = 6 - x^2 represents a function, we need to check if there is a unique y-value for each x-value.

Given the equation, we can solve for y by taking the square root of both sides:

y = ±√(6 - x^2)

The ± symbol indicates that there are two possible y-values for each x-value. Thus, the equation does not represent a function because it fails the vertical line test.

In a function, for each x-value, there should be only one corresponding y-value. However, in this case, there are two distinct y-values. Therefore, y^2 = 6 - x^2 does not represent a function.

To determine whether the equation y^2 = 6 - x^2 represents a function, you need to verify if there is a unique y-value for every x-value.

To do this, we'll use the vertical line test. The test involves drawing vertical lines at different x-values and checking if each line intersects the graph of the equation at only one point.

In the given equation, y^2 = 6 - x^2, you can rewrite it as two separate equations:
1. y = √(6 - x^2)
2. y = -√(6 - x^2)

Now, for each x-value, you can calculate the corresponding y-values by substituting it into both equations.

For example, let's choose x = 2:
1. y = √(6 - 2^2) = √(6 - 4) = √2
2. y = -√(6 - 2^2) = -√(6 - 4) = -√2

As you can see, for x = 2, there are two different y-values (both √2 and -√2). This violates the vertical line test, which means the equation does not represent a function.

In conclusion, y^2 = 6 - x^2 does not represent a function because it fails the vertical line test; there are x-values for which there are multiple corresponding y-values.