Trying to understand what the differnce is between a vertical and horizontal line test. If an equation fails the vertical line test, what does that tell you about the graph? If an equation fails the

Jun 12, 2018 · However, to me that doesn't seem to make much sense as we could simply define a bivariate function like f(x, y) f (x, y) as having two inputs instead. Is there an intuitive way to understand this? Relevant threads: Confusion with the vertical line test of functions Difference between horizontal and vertical line tests. Vertical line test

If you are given the domain, then when you apply the vertical line test, you require that, for each x x in the domain there is exactly one y y such that (x, y) (x, y) is in the function.

Oct 14, 2016 · If we plotted the rose petal function in the θ, r θ, r -plane, we would see that this function did indeed pass the vertical line test, and is a well-defined function. See here for a glimpse of what these "petal" functions look like in the θ, r θ, r -plane so you can see how these functions actually do pass the vertical line test.

More accurately: A curve in the xy x y -plane is a function of the variable x x if and only if it satisfies the vertical line test. The graphed parabola is not a function of x, x, because it fails the vertical line test. As a side note, it is still a function, but it is a function of y y (because it passes the horizontal line test).

Feb 23, 2024 · Horizontal line test is a test used to determine whether a function is injective (i.e., one-to-one). However, I read many answers that to determine whether f f has an inverse we should apply horizontal line test.

Feb 15, 2017 · is there any other way to just check, not prove, if a function is injective without this horizontal line test? I could not find any other ways online...

Sep 10, 2020 · Pretty much just the title. Obviously a vertical line isn't a function (doesn't pass the vertical line test), but technically it passes the horizontal line test for injectivity.

Jan 18, 2021 · A vertical line is the set of all points (x0, y) (x 0, y) where x0 x 0 is a fixed constant and y y is allowed to vary freely. Given an equation in the form f(x, y) = 0 f (x, y) = 0, we say it passes the vertical line test if, for every fixed choice of x0 x 0, the resulting equation f(x0, y) = 0 f (x 0, y) = 0 has either 0 0 or 1 1 solutions in terms of y y. For example, if we were checking the ...

The highlighted proposition is one way of describing the vertical line test, which determines whether f f is a function. If there is one and only point of intersection between x = a x = a and f(x) f (x), then f f is a function. If there are two or more points of intersection between x = a x = a and f(x) f (x), then f f maps a given x = a x = a to two (or more) distinct values, f(a) = b, f(a ...