The intervals of a piecewise are not unique because a function can produce more than one 𝑦−𝑦−value for the same 𝑥−𝑥−value.Question 1Select one:TrueFalse

Question Analysis

The question is asking whether the intervals of a piecewise function are unique, given that a function can produce multiple $y$ values for the same $x$ value.

Understanding Piecewise Functions

1. A piecewise function is defined by different expressions for different intervals of the independent variable $x$.
2. However, in the context of piecewise functions, for a given $x$ value, the function will return only one $y$ value for that $x$.

Answer Evaluation

• If a function can produce more than one $y$ value for the same $x$ value, it does not qualify as a function according to the definition in mathematics. Therefore, piecewise functions must provide a unique output for each input within their defined intervals.

Final Answer

False. The intervals of a piecewise function are unique for each segment, and a valid function cannot produce more than one $y$ value for the same $x$ value.