parabola image The Image above says that for every value of x in that first parabola curve, There is a distinct value of y but I fail to understand how could that be when at almost every single point of y, there are 2 values of x, one is in negative and the other one is in positive. so y isn't distinct for every value of x. correct?
Please help me understand where or how I am wrong in this as the book can't possibly be wrong I think.
Thanks for any help.
The text is referring to the first diagram, and it is saying that for each x value, there is a single y value. So if I asked you "When $x = 4$, what is $y$?", you would be able to give a single answer with no ambiguity. The text refers to the "vertical line test", which is simply "If you draw a vertical line on the graph, it will only ever intersect the curve once (if at all)". A curve that passes that test is a function.
The converse is not true, and I think that's what you're getting confused with - for each y, value, there is not necessarily a distinct x value, meaning that the parabola does not pass the horizontal line test which means that the parabola is not defined by a one-to-one (or injective) function.