![]() ![]() This process doesn't have to be "algebraic" it is just "clear" (or "rigorous") (more so than looking at a picture at least). A graph is said to be a function if the vertical line drawn does not. For a relation or graph to be a function, it can have at most. $f(x) = x^2$ 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. Vertical Line Test is a test used to determine whether a relation is a function or not. The vertical line test is a test to determine if a relation or its graph is a function or not. For example, on the interval /2, /2, y sin x is one-to-one and therefore. In order to be a function, each x value can. However, if you take a small section, the function does have an inverse. The Vertical Line Test is a visual test that you can use to quickly check and see if a graph represents a function. ![]() For example, at first glance sin x should not have an inverse, because it doesn’t pass the horizontal line test. 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 horizontal line test can get a little tricky for specific functions. Any vertical line can touch the graph at most once. There are many different possibilities for this answer, but whatever graph you choose to draw must pass the Vertical Line Test. Create a graph that represents a function and explain why it’s a function. In practice, this typically amounts to checking how the "relation" is defined, and comparing it with this "exactly one" condition. How to use the Vertical Line Test to verify whether a graph is a function. If you think about it, the vertical line test is simply a restatement of the definition of a function. Math help video explaining Algebra concepts using example problems. states that if a vertical line intersects the graph of the relation more than once, then the relation is a NOT a function. How to determine whether a graph is a function using the vertical line test. This time you draw a horizontal line, and if the line touches the original function in more. 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. is a way to determine if a relation is a function. The horizontal line test works similar to the vertical line test. ![]()
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