their distance from home as a function of time
[tex]f(x)=50x+20[/tex]
The reasonable domain for this situation is
[tex]0\leq x\leq 2[/tex]
Given :
Aubrey and Charlie are driving to a city that is 120 miles from their house. They have already traveled 20 miles, and they are driving at a constant rate of 50 mi/h.
Given driving speed is 50 miles per hour
They already travelled 20 miles. We need to frame linear equation because we are given with constant rate.
Linear equation is [tex]f(x)=mx+b[/tex]
where m is the constant rate and b is the initial miles travelled
m=50 and b=20
the function f(x) is the distance from home
[tex]f(x)= 50x+20[/tex]
Now we find out the domain x. Given that they travelled 120 miles
so f(x) is 120
[tex]120=50x+20\\120-20=50x\\100=5x\\x=2[/tex]
Domain is the number of hours travelled
hours cannot be negative . So the domain x for this situation is
[tex]0\leq x\leq 2[/tex]
Learn more : brainly.com/question/6370880
