SOLUTION: For what value(s) of k will the relation not be a function? B = {(0.5k-5, 10), (k+7, 4)}

Question 1100839: For what value(s) of k will the relation not be a function? B = {(0.5k-5, 10), (k+7, 4)}
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

The relation will NOT be a function if the inputs are equal. Repeated inputs leading to different outputs mean we won't have a function. In other words, a function is only possible if for any given input, there is exactly one output

Set the inputs 0.5k-5 and k+7 equal to each other. Then solve for k

0.5k-5 = k+7
0.5k-5-0.5k = k+7-0.5k
-5 = 0.5k+7
-5-7 = 0.5k+7-7
-12 = 0.5k
0.5k = -12
0.5k/0.5 = -12/0.5
k = -24

So if k = -24, then the expressions 0.5k-5 and k+7 will be equal to each other. What will they be equal to? Let's find out
k+7 = -24+7 = -17
0.5*k-5 = 0.5*(-24)-5 = -12-5 = -17
Both inputs will be equal to -17 if k = -24

The relation B = {(0.5k-5, 10), (k+7, 4)} will update to B = {(-17, 10), (-17, 4)} when k = -24. This relation is NOT a function due to the fact the input x = -17 leads to more than one output (y = 10 and y = 4 at the same time).

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