f(x) = x2
This is a function by the vertical line test because a vertical line drawn through this function will only intersect the function at one point
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Horizonatal line test is a test use to determine if a function is one-to-one. If a horizontal line intersects a function's graph more than once, then the function is not one-to-one. A one-to-one function is a function where every element of the range correspons to exactly one element of the domain. Vertical line test is a test used to determine if a function is a function or relation. If you can put a vertical line through graph and it only hits the graph once, then it is a function. If it hits more than once, then it is a relation.
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The "vertical line test" will tell you if it is a function or not. The graph is not a function if it is possible to draw a vertical line through two points.
Functions cannot have two y-values (outputs) for any single x-value (input), so if you can draw a vertical line that touches more than 1 point on the graph, it is not a function.
You use the "vertical line test". If anywhere you can draw a vertical line that goes through two points of the graph, the relation is not a function; otherwise, it is a function. This is just another way of saying that in a function for every x value (input) there is AT MOST one y value (output).