To determine the domain and range of the data and whether it represents a functional relationship, we need to understand the terms involved.
- Domain: This refers to the set of all possible input values (in this case, heights).
- Range: This refers to the set of all possible output values (in this case, shoe sizes).
- Functional Relationship: A relationship is functional if each input (height) corresponds to exactly one output (shoe size).
Given Data:
- Heights: {5'10", 9, 5'11", 9.5, 5'9", 8.5}
- Shoe Sizes: {9, 9.5, 8.5, 12, 10, 11.5}
Domain and Range:
-
Domain (Heights): The set of heights can be looked at as:
- 5'10" (converted to a numeric value could be approximately 70 inches)
- 5'11" (approximately 71 inches)
- 5'9" (approximately 69 inches)
- 9 (interpreted as a numeric height in inches)
- 9.5 (interpreted similarly)
- 8.5 (interpreted similarly)
Domain = {5'10", 9, 5'11", 9.5, 5'9", 8.5} or {69, 70, 71, 9, 9.5, 8.5} (in numeric form)
-
Range (Shoe Sizes): The set of shoe sizes is:
- 9
- 9.5
- 8.5
- 12
- 10
- 11.5
Range = {9, 9.5, 8.5, 12, 10, 11.5}
Functional Relationship:
To check for a functional relationship, we need to see whether any height corresponds to more than one shoe size.
- If we analyze the heights and shoe sizes given, we see that there are multiple heights (particularly the numeric height values) without specific shoe size assignments. For example, we cannot determine how many people have a height of 9 or 9.5, and without additional data or assignments, we cannot confirm that each height corresponds to a unique shoe size.
Conclusion:
- Domain: {5'10", 9, 5'11", 9.5, 5'9", 8.5}
- Range: {9, 9.5, 8.5, 12, 10, 11.5}
- As it stands, this data does not represent a functional relationship because we cannot ascertain a unique shoe size for each height based solely on the information provided. Different heights could map to the same shoe size or vice versa, leading to multiple outputs for the same input.