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).
, we have for 
the Taylor series expansion about 0 as
with 
, so that the series is equivalent to
, we have
