This principle is referred to as the horizontal line test. Every one x in X maps to exactly one unique y in Y. The circled parts of the axes represent domain and range sets— in accordance with the standard diagrams above. Not an injective function. Here X1 and X2 are subsets of X, Y1 and Y2 are subsets of Y: for two regions where the function is not injective because more than one domain element can map to a single range element.
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Injective, Surjective and Bijective "Injective, Surjective and Bijective" tells us about how a function behaves. As it is also a function one-to-many is not OK But we can have a "B" without a matching "A" Injective is also called "One-to-One" Surjective means that every "B" has at least one matching "A" maybe more than one. Bijective means both Injective and Surjective together. Think of it as a "perfect pairing" between the sets: every one has a partner and no one is left out. So there is a perfect "one-to-one correspondence" between the members of the sets.
Bijective functions have an inverse! If every "A" goes to a unique "B", and every "B" has a matching "A" then we can go back and forwards without being led astray. Read Inverse Functions for more. On A Graph So let us see a few examples to understand what is going on.
When A and B are subsets of the Real Numbers we can graph the relationship. Let us have A on the x axis and B on y, and look at our first example: This is not a function because we have an A with many B.
For example sine, cosine, etc are like that. Perfectly valid functions. But an "Injective Function" is stricter, and looks like this: "Injective" one-to-one In fact we can do a "Horizontal Line Test": To be Injective, a Horizontal Line should never intersect the curve at 2 or more points. In simple terms: every B has some A. Thus it is also bijective.
Injective, Surjective and Bijective