Is this a onto function?

Ok I can't give a formula for it cause my mind is blank now. But is the function where the negative half of the y axis is the asymptote, on the positive side of the y it curves toward the positive side of the x axis to infinity.

It this an onto function.

Ok in a graphic calculator it looks is y=-1/x +5... But only the the graph on the right hand side, going toward x axis infinity.

2 Answers

  • 9 years ago
    Favorite Answer

    An "onto" function is one where every single element of the receiving set is used. If you are considering ALL the real numbers, and your graph only exists above the x-axis (it nevers goes below y=0) then none of the negative numbers get used as answers. The function is not onto.

    However, if you are talking about a function such as 1/x + something, this means that the graph on one side uses up all the y values above the something, and on the other side, the graph uses up all the y values below the something, then the question to ask is: does it use y = something?

    If there is a horizontal asymptote, that usually means that there is one value of y that is never reached (the value of y at the horizontal aymptote). Therefore, the "range" does not use all of y.

    But, if you define the target set as "all the real numebrs except that one value", then all the values of the receiving set will be used, and that could make it "onto".

    Onto is defined in relation to the receiving set.

  • 9 years ago

    Onto what range?

    If the range is all real numbers, then y = -1/x + 5 is not onto because no value of x will yield y = 5.

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