NeroRPG
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Determine the truth value of the following conjecture. If the conjecture is false, provide a counterexample.

Given: y = |3x+7|
Conjecture: y is always even.

A.
true
B.
false; absolute value of anything is always odd
C.
false; when x = –3, y is odd
D.
false; when x = 2, y is odd

Respuesta :

carlosego
For this case we have the following function:
 y = | 3x + 7 |
 We observe that the proposition "y is always even" is false.
 To prove it, it is sufficient to evaluate the function for x = 2.
 Evaluating the function we have:
 y = | 3 (2) +7 |
 Rewriting we have:
 y = | 6 + 7 |
 y = | 13 |
 y = 13
 We observe that the value of y is odd.
 Answer:
 D.
 false; when x = 2, y is odd

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