The function f: R !R given by f(x) = x2 is not injective as, e.g., ( 21) = 12 = 1. If a horizontal line can intersect the graph of the function only a single time, then the function … A few quick rules for identifying injective functions: With this test, you can see if any horizontal line drawn through the graph cuts through the function more than one time. In the example shown, =+2 is surjective as the horizontal line crosses the function … The first is not a function because if we imagine that it is traversed by a vertical line, it will cut the graph in two points. If a horizontal line intersects the graph of the function, more than one time, then the function is not mapped as one-to-one. The second graph and the third graph are results of functions because the imaginary vertical line does not cross the graphs more than once. \$\begingroup\$ See Horizontal line test: "we can decide if it is injective by looking at horizontal lines that intersect the function's graph." The \horizontal line test" is a (simplistic) tool used to determine if a function f: R !R is injective. Horizontal Line Testing for Surjectivity. An injective function can be determined by the horizontal line test or geometric test. Look for areas where the function crosses a horizontal line in at least two places; If this happens, then the function changes direction (e.g. The horizontal line test lets you know if a certain function has an inverse function, and if that inverse is also a function. Examples: An example of a relation that is not a function ... An example of a surjective function … Injective = one-to-one = monic : we say f:A –> B is one-to-one if “f passes a horizontal line test”. "Line Tests": The \vertical line test" is a (simplistic) tool used to determine if a relation f: R !R is function. 2. Example. You can find out if a function is injective by graphing it.An injective function must be continually increasing, or continually decreasing. If f(a1) = f(a2) then a1=a2. If no horizontal line intersects the function in more than one point, the function is one-to-one (or injective). Example picture (not a function): (8) Note: When defining a function it is important to limit the function (set x border values) because borders depend on the surjectivness, injectivness, bijectivness. This means that every output has only one corresponding input. You can also use a Horizontal Line Test to check if a function is surjective. ex: f:R –> R. y = e^x This function passes the vertical line test, but B ≠ R, so this function is injective but not surjective. The horizontal line test, which tests if any horizontal line intersects a graph at more than one point, can have three different results when applied to functions: 1. 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