Which of the following relations is a function?
  • (0,4), (-2, 6), (0, 3), (-7, 2)
     
  • (7,1), (-2, 4), (0, 1), (7, 2)
     
  • (0,4), (-2, 2), (7, 1), (-7, 2)
     
  • (0,0), (-2, 3), (7, 1), (-2, 5)

 

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1 Answer

A function maps the independent variable to the dependent variable uniquely, that is, f(x) maps to one and only one value of y, although a particular y value can be mapped by different values of x.

In (1) we have (0,4) and (0,3), zero maps to two different values, so it's not a function.

In (2) we have (7,1) and (7,2), also not a function.

In (3) there are no duplicate values of x to different values of y, so this is a function.

In (4) we have (-2,3) and (-2,5), which is not a function.

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