ExplanationThis function defines a made-up symbol: ~x is equivalent to |14x|. The question asks which statements must be true, so test each one:

~2 = ~(–2)

|14(2)| = |14(–2)|

|28| = |–28|

28 = 28

This first statement must be TRUE.Similarly, test the second statement:

~3 + ~4 = ~7

|14(3)| + |14(4)| = |14(7)|

42 + 56 = 98

98 = 98

This second statement must be TRUE.Finally, the third statement is also TRUE. Since ~x is equal to a statement inside an absolute value, this value can never be negative. If x = 0, then the value of |14x| is also 0. The minimum possible value for ~x is 0.

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Sandy

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