To determine the appropriate representations for the domain of a function that describes the number of weeks worked in a year, we need to consider the possible values for the variable representing the weeks worked.
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x is greater than or equal to 0: This is a valid representation because you cannot work a negative number of weeks.
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left bracket 0 comma infinity right parenthesis: This implies that working an infinite number of weeks is possible, which is not realistic in the context of weeks in a year. Therefore, this representation is not appropriate.
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open paren negative infinity comma infinity close paren: This representation suggests that any value of weeks worked, including negative values and infinitely large values, is possible. This is not valid for the domain of weeks worked, so it is not appropriate.
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left bracket 0 comma 52 right bracket: This representation indicates that the number of weeks worked can range from 0 to 52 weeks inclusive, which accurately reflects the situation (as there are 52 weeks in a year). This is a valid representation.
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open paren 0 comma 52 close paren: This representation would imply that you cannot work 0 weeks or 52 weeks, which is not correct. Therefore, this representation is not appropriate.
In summary, the valid representations for the domain of a function given by the number of weeks worked in a year are:
- x is greater than or equal to 0
- left bracket 0 comma 52 right bracket
1 answer