For example, on the interval /2, /2, y sin x is one-to-one and therefore. The vertical line test states that a relation is a function iff. A graph will be considered as a function if it. This is also called a vertical line test. This visual exam consists of testing multiple vertical lines against the graph an equation and seeing. It would be a function if all vertical lines intersect it minimum once. Let's look at a couple of examples to clarify this definition. The vertical line test is a way of determining whether or not a plotted graph is a function. The vertical line test is a visual exam that allows for the quick identification of a function. However, in a function, each input (x coordinate) may be paired with only ONE output (y coordinate). However, if you take a small section, the function does have an inverse. Using the Vertical Line Test A function is a relation (a set of ordered pairs) where the value of one variable depends on the value of the other variable. For example, at first glance sin x should not have an inverse, because it doesn’t pass the horizontal line test. In fact, circles can never represent functions, because they never pass the Vertical Line Test. The horizontal line test can get a little tricky for specific functions. If we can draw any vertical line that intersects a graph more than once, then the graph does not define a function because a function has only one output value for each input value. You know that the circle below doesn’t represent a function, because any vertical line you draw at some ?x? that’s strictly between ?-2? and ?2? (not “right at” ?-2? or ?2?) will cross the graph twice, which causes the graph to fail the Vertical Line Test. The vertical line test can be used to determine whether a graph represents a function. If some vertical line crosses the graph more than once, then the graph has failed the Vertical Line Test and the relation isn’t a function. Note: Even graphs need to worry about tests Using the vertical line test, you can figure out if a graph is a function or not. Visually, when you look at the graph of a relation, you can see whether every ?x?-value is related to only one ?y?-value by using the Vertical Line Test: Any (and every possible) vertical line may intersect (cross) the graph at most once. To test for functions, we need to make sure that there’s only one ?y?-value for every ?x?-value. You know that a relation is not a function if there is at least one value of ?x? that’s related to two different values of ?y?. Passing the Vertical Line Test also implies that the graph has only one output ?y? for any input ?x?.
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