Question

You are 330 miles from home and you are driving toward home at an average of 55 mph. Write an equation to represent the situation and find the domain and range of the function.

Answer 1

55x=330. so x=6 the domain is 6 because its the input and 330 is the range because its the outpt

Answer 2

D∈[0,6] R∈ [330,0]

Explanation:

Analyzing the data:

Average Speed: 55 miles per hour

Location: 330 miles

Well, those two physical quantities speed and space already relate to each other in this formula:

`Vm=(Δs)/(Δt)`

`55=(330-0)/(Δt)`

`55t=330\\`

Rewriting it as a function

`s=330-55t\\`

Domain. The inputs for our Domain are going to be: the hours needed to get back home. Since this question imposes us some restrictions, the hours enough to get home, and as there is no negative hour.

0=330-55t

330=-55t

t=6 hours

So we can write

D∈[0,6]

Range. As for the Range of this function, we will call it the location. All we have to do is to find the Interval where it is valid this function, under those conditions.

Since it is a decreasing function. It all starts with position 330 miles and then goes all the way to point 0 (home). So we can say that: R ∈ [330,0]