53. Determine if y=x^2 is a function.

i think the answer is yes, but can someone explain to me why it's yes, and how you find out if it's a function or not.

I know that for every value of x there should be one value of y, but how do you figure that out in a problem like this?

for any x, you get a specific y. It is a function. Now for any x, you get more than one y, it is not a function.

So, this one is a function..? because for x you get only one y

Yes, if any x maps to one specific y, it is a function.

To determine if a given equation defines a function, you need to check if for each input value of 'x', there is a unique output value of 'y'. In the equation y = x^2, we can see that it represents a quadratic function.

To check if this function is a valid one, you can use the vertical line test. The vertical line test states that if you can draw a vertical line through the graph of the equation and it intersects the graph at more than one point, then it is not a function.

For the equation y = x^2, if you try to draw a vertical line through any part of the graph, it will only intersect the graph at one point. Therefore, the equation y = x^2 is indeed a function.

To further understand how the graph of y = x^2 represents a function, you can observe that for every value of x, there is indeed one unique value of y. For example, if x is 2, then y = (2)^2 = 4. If x is -2, then y = (-2)^2 = 4. So, each value of x corresponds to a unique value of y.

In summary, the equation y = x^2 is a function because it passes the vertical line test, and for every value of x, there is exactly one corresponding value of y.