Question

select the correct answer.
carly is traveling to visit family. she drives x miles on the first day and y miles on the second day for a total of 800 miles.
what are the domain and range of this relationship?

• domain: ( 0 leq x leq 800 )

range: ( 0 leq y leq 800 )

• domain: ( 0 leq x leq 400 )

range: ( 1 leq y leq 400 )

• domain: ( x geq 0 )

range: ( y geq 0 )

• domain: ( x leq 800 )

range: ( y leq 800 )

Explanation:

Step1: Analyze the relationship

We know that \(x + y=800\), so we can rewrite it as \(y = 800 - x\). Since the number of miles driven can't be negative, we have \(x\geq0\) and \(y = 800 - x\geq0\), which implies \(x\leq800\). So for the domain (values of \(x\)), we have \(0\leq x\leq800\).

Step2: Analyze the range (values of \(y\))

From \(y=800 - x\) and \(0\leq x\leq800\), when \(x = 0\), \(y=800\); when \(x = 800\), \(y = 0\). So \(0\leq y\leq800\).
Looking at the options, the first option has domain \(0\leq x\leq800\) and range \(0\leq y\leq800\).

Answer:

A. domain: \(0\leq x\leq800\)
range: \(0\leq y\leq800\) (assuming the first option is labeled as A with this content)