Question

The set of ordered pairs shown represents a function, f,

{(–5, 3), (4, 9), (3, –2), (0, 6)}


Select THREE ordered pairs that could be added to the set that would allow f to remain a function.


Question 10 options:


A)


(-3, -2)



B)


(4, 0)



C)


(0, -1)



D)


(1, 6)



E)


(2, 3)



F)


(-5, 9)

Answer 1

The correct options are A, D and E.

Explanation:

The given set of ordered pairs represents a function

`f=\{(-5, 3), (4, 9), (3, -2), (0, 6)\}`

We need to find THREE ordered pairs that could be added to the set that would allow f to remain a function.

A relation is a function if there exist unique value of y for each value of x.

The x values for given function are -5, 4, 3 and 0.

If we add (-3,-2) in the given set, then we unique value of y for each value of x. So, option A is correct.

If we add (4,0) in the given set, then we have y=0 and y=9 at x=4. Since the set have more than one value of y for same x-value, therefore option B is incorrect.

If we add (0,-1) in the given set, then we have y=-1 and y=6 at x=0. Since the set have more than one value of y for same x-value, therefore option C is incorrect.

If we add (1,6) in the given set, then we unique value of y for each value of x. So, option D is correct.

If we add (2,3) in the given set, then we unique value of y for each value of x. So, option E is correct.

If we add (-5,9) in the given set, then we have y=9 and y=3 at x=-5. Since the set have more than one value of y for same x-value, therefore option F is incorrect.

Therefore the correct options are A, D and E.

Answer 2

B) (4, 0)

C) (0, -1)

E) (2, 3)

Explanation:

If we see the rule of function then it says that,

a function is a special relationship where each input, x, has a single output, y.

It means that for every value of x there SHOULD be a different value of y.

A)

(-3,-2) Rejected

because when x = 3, y = -2

D)

(1, 6) Rejected

because when x = 0, y = 6

F)

(-5, 9) Rejected

because when x = 4, y = 9