Mathematical Modeling: Part Three — Test

Question 7 • Mathematics III

Which piecewise relation defines a function?

Answer

y equals enlarged left-brace first row x squared comma x less than negative 2. Second row 0 comma negative 2 less than or equal to x less than or equal to 4. Third row negative x squared comma x greater than or equal to 4.

y equals enlarged left-brace first row negative 3 x comma x less than negative 2. Second row 3 comma 0 less than or equal to x less than 4. Third row 2 x comma x greater than or equal to 4.

y equals enlarged left-brace first row x squared comma x less than or equal to negative 2. Second row 4 comma negative 2 less than x less than or equal to 2. Third row x squared plus 1 comma x greater than or equal to 2.

y equals enlarged left-brace first row negative 3 x comma x less than negative 4. Second row 3 comma negative 5 less than x less than 1. Third row 2 x comma x greater than or equal to 1.

Explanation

A relation defines a function when no input x is assigned more than one output. In choice B, the intervals x < −2, 0 ≤ x < 4, and x ≥ 4 do not overlap, so no input receives two outputs. Some x-values are not included, but that does not prevent the relation from being a function. The other choices have overlapping intervals that assign conflicting outputs to at least one x-value.

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