First, we need to understand the relationship given in the problem:
Carly drives [tex]$x$[/tex] miles on the first day and [tex]$y$[/tex] miles on the second day, for a total of 800 miles. Mathematically, we can express this relationship as:
[tex]\[ x + y = 800 \][/tex]
To find the domain and range of this relationship, we need to consider the possible values of [tex]$x$[/tex] and [tex]$y$[/tex].
### Domain:
The domain represents all possible values of [tex]$x$[/tex] that Carly can drive on the first day. Because Carly cannot drive a negative distance, [tex]$x$[/tex] must be greater than or equal to 0. Additionally, since the total distance must be 800 miles and Carly completes her trip in two days, the farthest she can drive in one day is the total distance of 800 miles. Thus, the domain for [tex]$x$[/tex] is:
[tex]\[ 0 \leq x \leq 800 \][/tex]
### Range:
The range represents all possible values of [tex]$y$[/tex] that Carly can drive on the second day. Similarly, because Carly cannot drive a negative distance, [tex]$y$[/tex] must be greater than or equal to 0. Since [tex]$x$[/tex] and [tex]$y$[/tex] sum to 800, the most she can drive on the second day, if she drives 0 miles on the first day, is the full 800 miles. Thus, the range for [tex]$y$[/tex] is:
[tex]\[ 0 \leq y \leq 800 \][/tex]
Therefore, the correct answer is:
- Domain: [tex]\( 0 \leq x \leq 800 \)[/tex]
- Range: [tex]\( 0 \leq y \leq 800 \)[/tex]
