The set of ordered pairs below represents a function. {(–9, 1), (–5, 2), (0, 7), (1, 3), (6, –10)}

Josiah claims that the ordered pair (6, –10) can be replaced with any ordered pair and the set will still represent a function.

Select all ordered pairs that could be used to show that this claim is incorrect.
(–9, –6)
(1, 12)
(–10, –10)
(4, 7)
(–5, 1)

Given:

The set of ordered pairs below represents a function.

{(–9, 1), (–5, 2), (0, 7), (1, 3), (6, –10)}

Josiah claims that the ordered pair (6, –10) can be replaced with any ordered pair and the set will still represent a function.

To find:

All the ordered pairs that could be used to show that this claim is incorrect.

Solution:

We need to find the ordered pairs that can be replaced with (6,-10) and for which the set is not a function.

A relation is called function if there exist a unique output for each input.

If (-9,-6) is replaces with (6,-10), then the set has two outputs y=1 and y=-6 for x=-9. So, the claim is incorrect.

If (1,12) is replaces with (6,-10), then the set has two outputs y=12 and y=3 for x=1. So, the claim is incorrect.

If (-10,-10) is replaces with (6,-10), then there exist unique output for each input. So, the claim is correct.

If (4,7) is replaces with (6,-10), then there exist unique output for each input. So, the claim is correct.

If (-5,1) is replaces with (6,-10), then the set has two outputs y=1 and y=2 for x=-5. So, the claim is incorrect.

Therefore, the correct options are (a), (b) and (e).

option 2 is correct.

step-by-step explanation:

we are given two inequality equation

x+y> 5 and -3x+2y< -2

first we draw the graph of both function using t-table method

equation: x+y> 5

for x=0, y=5

for x=-5, y=0

table:

x   :   0     5

y   :   5     0

test point (0,0) , 0> 5

false

equation: -3x+2y< -2

for x=0, y=-1

for x=2, y=4

table:

x   :   0     2

y   : -1       4

test point (0,0) , 0< -2

true

now we draw the graph. see the attachment for graph.

common region would be solution set.

option 2 is correct.