a. Table
Year Average House Value ($)
2014 254,000
2015 293,000
2016 338,000
2017 72,000
b. The domain is {2014,2015,2016,2017}.
The range is {254,000,293,000,338,000,372,000}.
c. Since each input is associated with a unique output, the relation is a function.
a. Table:
The table organizes the given data in a clear format, with years listed in one column and corresponding average house values in another.
This makes it easier to visualize and analyze the information.
The data suggests an upward trend, indicating an increase in average house values over the specified years.
b. Domain and Range:
Domain: In mathematical terms, the domain is the set of input values. In this context, the years (2014, 2015, 2016, 2017) serve as input values.
The domain is the collection of these years, represented as {2014,2015,2016,2017}.
Range: The range, on the other hand, is the set of output values. Here, the average house values are the outputs.
The range is given as
{254,000,293,000,338,000,372,000}.
It reflects the changing average values of houses in Denver over the specified years.
c. Functionality:
A function is a relation where each input is associated with exactly one output. In the context of average house values, this means that each year should correspond to a unique average house value. Examining the provided data:
For the year 2014, the average house value is $254,000.
For the year 2015, the average house value is $293,000.
For the year 2016, the average house value is $338,000.
For the year 2017, the average house value is $372,000.
Since each year is paired with a distinct average house value, the relation fulfills the criteria of a function. This confirms that there is a consistent, one-to-one mapping between the years and their respective average house values.
The table presents a clear representation of the average house values in Denver from 2014 to 2017. The domain consists of the years, the range consists of the average house values, and the relation is a function due to the unique mapping of each year to its corresponding average house value
Question
The average value of a house changes over time. The average
values of a house in January in Denver, Colorado, for different years are as follows: 2014, $254,000; 2015, $293,000; 2016, $338,000; 2017, $372,000.
a. Make a table.
b. Determine the domain and range of the relation.
c. Determine whether the relation is a function.