Question

1. the table shows a relation between x, the number of dvds rented and y, the cost in dollars.

dvd rentals

number of dvds rented, x	cost (in dollars), y
4	12
8	16

what is the range of this relation?
a. {2, 4, 8, 12, 16}
b. {2, 4, 8}
c. {8, 12, 16}
d. {8, 16}

Explanation:

Step1: Recall the definition of range

The range of a relation is the set of all the output values (the \( y \)-values) of the relation.

Step2: Identify the \( y \)-values from the table

From the table, the \( y \)-values (cost in dollars) are 8, 12, and 16.

Step3: Form the set of these \( y \)-values

The set containing these values is \(\{8, 12, 16\}\) (note: there was a typo in option C, it should be 16 instead of 10? Wait, looking at the table, when \( x = 8 \), \( y = 16 \), when \( x = 4 \), \( y = 12 \), when \( x = 2 \), \( y = 8 \). So the \( y \)-values are 8, 12, 16. So the range is \(\{8, 12, 16\}\), which corresponds to option C (assuming the 10 is a typo and should be 16).

Answer:

C. \(\{8, 12, 16\}\)