Question

For what value(s) of k will the relation not be a function? S={(2-|k+1|,4), (-6,7)}

Answer 1

A relation is the relationship between variables. When each input has one output, the relation is a function. When the value of k is 5 or 3, the relation will not be a function.

Given that:

$S= \{(2-|k+1|,4), (-6,7)\}$

For S, not to be a function, 1 domain element must point to more than one range elements.

This means that:

$2-|k+1| = 6$

Collect like terms

$-|k+1| = 6 - 2$

$-|k+1| = 4$

Multiply by -1

$|k+1| = -4$

Remove absolute bracket

$k+1 = -4\ or\ k+1 = 4$

Solve for k

$k =-1 -4\ or\ k= -1+4$

$k =-5\ or\ k= 3$

Hence, when k is 5 or 3, the relation will not be a function.

Read more about functions and relations at:

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