Question

Determine if the equation represents y as a function of x.

Answer 1

(x-2)^(2)+y^(2)=4

Answer 2

Let me ask you, what does it take for an equation to NOT represent y as a function of x?

Answer 3

The values to not equal?

Answer 4

No, I was looking for something along the lines of having only one value of y associated with one value of x.

For this equation, consider \(x=2\). (Reason for this is to eliminate x from the equation and focus on just the y)

Now you have
\[(2-2)^2+y^2=4\\
y^2=4\]
Now, there are two solutions for y, \(y=2\) and \(y=-2\). This means for one values of x \((x=2)\), you have two values of y.

Does that mean y is a function of x?

Answer 5

yes?

Answer 6

No. It's not.

Answer 7

You have two values of y for one value of x.

Any time you have more than one y for only one x, you do not have a function.