Math Problem Statement
Solution
The problem presents a function that models the distance in kilometers Kellen runs, where is the time in hours. The given conditions specify that Kellen runs for at least 1 hour but no more than 2 hours.
To determine the domains:
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Theoretical Domain: The theoretical domain refers to all possible values of that the function could take, regardless of real-world constraints. Since is a linear function with no restrictions based on the equation itself, the theoretical domain could be all real numbers (i.e., ).
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Practical Domain: The practical domain refers to the real-world constraints given in the problem. Kellen runs for a time between 1 hour and 2 hours, inclusive. So, the practical domain is [1, 2], meaning can be any real number between 1 and 2, inclusive.
Correct answers:
- The theoretical domain is all real numbers.
- The practical domain is all real numbers between 1 and 2, inclusive.
Would you like further clarification or details on this?
Here are 5 related questions to explore this topic further:
- How would the range of the function change if Kellen’s running speed was different?
- What is the distance Kellen runs if he runs for exactly 1.5 hours?
- How would you graph the function on a coordinate plane?
- What would the practical domain be if the time limit changed to 0.5 hours to 3 hours?
- How do theoretical and practical domains differ in real-world problems?
Tip: Always check for any real-world constraints when determining the practical domain in applied mathematics problems.
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Math Problem Analysis
Mathematical Concepts
Functions
Domain of a Function
Linear Functions
Formulas
d(t) = 6.6t
Theorems
Domain of a Function
Suitable Grade Level
Grades 9-11
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