Final answer:
The relation R will not be a function when k is approximately 3.132 because this value would make both x-values of the ordered pairs the same, which contradicts the definition of a function.
Step-by-step explanation:
To determine for what value of k the relation R will not be a function, we look at whether any x-values (first elements in the ordered pairs) repeat because a function can have only one output per input. The relation R is given as R={(k-8.3+2.4k,-5),(3/4k,4)}. To be a function, the x-values must be different, which means that k-8.3+2.4k must not equal 3/4k.
Combine like terms in the first coordinate of the first ordered pair:
k - 8.3 + 2.4k = 3.4k - 8.3.
Now set this equal to the first coordinate of the second ordered pair and solve for k:
3.4k - 8.3 = 3/4k.
3.4k - 3/4k = 8.3.
(3.4 - 0.75)k = 8.3.
2.65k = 8.3.
k ≈ 3.132.
So the relation will not be a function when k ≈ 3.132 since this would make both x-values of the ordered pairs equal, violating the definition of a function.