Question

Removing which ordered pair from the table would make the relation a function of x?

x y
1 7
4 7
2 2
4 1
3 9


(1, 7)
(2, 2)
(3, 9)
(4, 1)

Answer 1

Option D. (4, 1)

Explanation:

We take an example of a linear function. If an equation is in the form of y = mx + c, then the equation will be a function when for a unique input value of x we get a unique output value of y.

Now in the given table all ordered pairs define a function except one.

We have to remove that ordered pair to make the relation a function of x.

Here for every value of x = 1, 4, 2, 4, 3 we should get a unique value of y, but for x = 4 we are getting y = 7 and 1 two values.

So one of the ordered pairs (4, 7) or (4, 1) should be removed to define the relation a function.

This may be true for any other function.

As given in the option (4, 1) should be removed.

Answer 2

A function is a relation that for each input value x takes the unique value of output y.

Consider the table

`\begin{array}{cc}x&y\\1&7\\4&7\\2&2\\4&1\\3&9\end{array}`

You can see that x=4 takes two different values y=7 and y=1. You should remove one of these ordered pairs (4,7) or (4,1).

Answer: correct choice is D