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Hi,

to determine if an equation represents a function you should do this thing called the "vertical line test" -- input a value for x. If multiple y values come out, then you do not have a function. One of the main definitions of a function is that for every x value, there is only one y value.

In the future, please go below your video or exercise and ask a question. This kind of post is not suited for the community help center, which is more for site issues, bugs, or general questions.

When you're solving an equation like (x - 3) = y^2, it's important to remember that taking the square root of both sides of the equation can introduce an extra solution that doesn't necessarily satisfy the original equation. When you take the square root of both sides of the equation, you get:

√(x - 3) = ±y

The ± sign indicates that there are two possible values of y that could satisfy the equation, one positive and one negative. This is because when you square a number, you get the same result whether the number is positive or negative. For example, (-2)^2 = 4 and (2)^2 = 4.

Now, let's look at your method of solving the equation:

(x - 3) = y * y
(x - 3) / y = y

When you divide both sides of the equation by y, you're essentially assuming that y is nonzero, since you can't divide by zero. However, this assumption doesn't account for the possibility of a negative value of y, which would make the division by y invalid. Therefore, your method of solving the equation doesn't consider all possible solutions.

To summarize, when you're solving an equation like (x - 3) = y^2, it's important to remember that taking the square root of both sides can introduce an extra solution, which explains why there are two possible values of y that satisfy the equation. Dividing both sides by y, on the other hand, assumes that y is nonzero and doesn't consider all possible solutions.