The table below lists some of the characteristics of the houses on Katrina’s street.

Question

Characteristics of Homes For Sale on Katrina’s Street
Bedrooms
Acres of land
Sale price
Appraised value
Property tax
2
0.17
$230,000
$200,000
$1,220
2
0.20
$210,000
$220,000
$1,232
3
0.20
$275,000
$250,000
$1,400
4
0.24
$275,000
$275,000
$1,540
4
0.52
$360,000
$310,000
$1,736
4
0.75
$350,000
$320,000
$1,792
5
1.23
$375,000
$350,000
$1,960

Which relationship describes a function?
(bedrooms, sale price)
(acres of land, appraised value)
(sale price, bedrooms)
(appraised value, property tax)

Answer 1

To determine which pairs of characteristics describe a function, we must identify whether one variable uniquely determines the other. This means that for each value of the first variable, there should be exactly one corresponding value of the second variable.

Let's analyze each pair:

1. (bedrooms, sale price):

   • Multiple homes have the same number of bedrooms, but they have different sale prices (e.g., two homes with 4 bedrooms have different sale prices). Therefore, this relationship does not describe a function.

2. (acres of land, appraised value):

   • Several homes with different appraised values can occur at the same acreage. For instance, one home with 0.20 acres has an appraised value of $220,000, and another home with 0.20 acres has an appraised value of $250,000. Thus, this relationship does not describe a function.

3. (sale price, bedrooms):

   • Similar to the first case, multiple homes with different sale prices can have the same number of bedrooms. Thus, this relationship does not describe a function.

4. (appraised value, property tax):

   • Here, we assess if unique property tax values correspond one-to-one with appraised values. In the data provided:
     • A home appraised at $200,000 has a property tax of $1,220.
     • A home appraised at $220,000 has a property tax of $1,232.
     • A home appraised at $250,000 has a property tax of $1,400.
     • A home appraised at $275,000 has a property tax of $1,540.
     • A home appraised at $310,000 has a property tax of $1,736.
     • A home appraised at $320,000 has a property tax of $1,792.
     • A home appraised at $350,000 has a property tax of $1,960.

   All appraised values correspond to unique property tax amounts, so this relationship describes a function.

Based on this analysis, the relationship that describes a function is:

(appraised value, property tax).