Which relationship describes a function?
(bedrooms, sale price)
(acres of land, appraised value)
(sale price, bedrooms)
(appraised value, property tax)
Answer (1)
A function requires each input to have only one output.
(Bedrooms, Sale Price) is not a function because 2 bedrooms can have different sale prices.
(Acres of Land, Appraised Value) is not a function because 0.20 acres can have different appraised values.
(Sale Price, Bedrooms) is not a function because $275,000 can correspond to different numbers of bedrooms.
(Appraised Value, Property Tax) is a function because each appraised value corresponds to a unique property tax.
The relationship that describes a function is (appraised value, property tax) .
Explanation
Analyzing the Relationships Let's analyze the given relationships to determine which one represents a function. A function requires that each input has only one output. We will examine each relationship individually.
Bedrooms vs. Sale Price
(Bedrooms, Sale Price):
2 bedrooms: $230,000, $210,000 (Two different sale prices for the same number of bedrooms) Since there are different sale prices for the same number of bedrooms (2), this relationship is not a function.
Acres of Land vs. Appraised Value
(Acres of Land, Appraised Value):
0.20 acres: $220,000, $250,000 (Two different appraised values for the same acreage) Since there are different appraised values for the same acreage (0.20), this relationship is not a function.
Sale Price vs. Bedrooms
(Sale Price, Bedrooms):
$275,000: 3 bedrooms, 4 bedrooms (Two different numbers of bedrooms for the same sale price) Since there are different numbers of bedrooms for the same sale price ($275,000), this relationship is not a function.
Appraised Value vs. Property Tax
(Appraised Value, Property Tax):
$200,000: $1,220
$220,000: $1,232
$250,000: $1,400
$275,000: $1,540
$310,000: $1,736
$320,000: $1,792
$350,000: $1,960 Each appraised value has a unique property tax. Therefore, this relationship is a function.
Conclusion Therefore, the relationship that describes a function is (appraised value, property tax).
Examples
In real estate, understanding functional relationships is crucial. For example, the relationship between the size of a house (in square feet) and its market value can often be modeled as a function. If each house size corresponds to a unique market value, it helps in predicting property values based on size. This is a simplified view, as other factors also influence property value, but it provides a foundational understanding for real estate analysis.
