What is the formula for a vertical line A vertical line has as a characteristic the fact that all x-values of its points are the. This process doesn't have to be "algebraic" it is just "clear" (or "rigorous") (more so than looking at a picture at least). The vertical line test tells if a curve is the graph of a function. Draw a vertical line and check if it intersects a curve on an XY plane more than once. $f(x) = x^2$ is another function, to check this is a function amounts to just checking that when you take any number x and square it, the output is unique (there is a single output, for example, -3 gets sent to the unique output $(-3)^2 = 9$) In this way, $x^2$ is a function. Take note that the vertical line test shall pass the following: The graph shall only have one output of y for every input of x. You can use the vertical line test on a graph to determine whether a relation is a. Let's say our "relation" is f(x) = x (so the "identity function", sends numbers to themselves), we start with a number a, and f sends this a to f(a), which is just a in this case, so we start with a, and this a gets sent just to a, so where the function sends any number a (to itself) is definitely unique. The Vertical Line Test Main Concept The requirement that each input to a function must produce exactly one output can be used to visually determine when a. If a vertical line intersects a curve on an. A function can only have one output, y, for each unique input, x. In mathematics, the vertical line test is a visual way to determine if a curve is a graph of a function or not. The abscissa shows the domain of the (to be tested) function. Let’s do an example with another equation. The vertical line test, shown graphically. ![]() If a graph passes the Vertical Line Test, it’s the graph of a function. ![]() In practice, this typically amounts to checking how the "relation" is defined, and comparing it with this "exactly one" condition. Every vertical line can only touch a graph once in order for the function to pass the Vertical Line Test. To say that a "relation" (or oftentimes "graph") is a "function" from A to B (A is the domain and B is the range) is to say that for any number a (in A) (so any number we take a "y value" at), there is exactly one number that this a gets mapped to.
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