Confusion regarding surjective function I am a high school student, today our teacher taught us about onto function, explain only thing that I understand 
What I have understand -- that is two values of $x$ have same value of $y$ mean $y=1$ is a onto function but how find the function is onto for the given different equations.
Edit - i have one more doubt regarding the same function
what my teacher told me that for every value of x there is value in set y am if i am right suppose set x contain 4 element and set y contain 3 element one one function is not possible if my above statement is right please correct me if i am wrong
Is parabola is always a onto function 
 A: Surjective is another word for onto. 
A function $$f:A\to B$$ is onto if for every $y\in B$ the exists at least one $x\in A$ such that $f(x)=y$
For example $f(x)=x^2$ is an onto function from $(-\infty, \infty) $ onto $[0, \infty)$
Because for every non negative real number $y$ we have $f(\sqrt x)=y$
A: I think that if you can understand this picture, then you can understand why a function from a set of four elements to a set of 3 elements cannot possibly be one-to-one (i.e injective).
https://img.yumpu.com/35419243/1/500x640/non-regular-languages-pigeonhole-principle-the-pigeonhole-.jpg
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If you can understand these pictures, I think you will understand the definition of one-to-one (injective) functions, onto (surjective) functions, etc..
https://www.mathsisfun.com/sets/images/function-mapping.svg
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Also, a remark to the other people who posted: I answered this question because I think it is quite mean for people to downvote a highschool student's sincere question. If you do not like the grammar, edit it rather than downvoting. 
