Question

A car travels at a rate of 45 miles per hour for 5 hour. Let y be the distance , in miles , the car travels for a given amount of time ,x, in hours. The situation can be modeled by a function. Which of these describe the domain of the function

Answer 1

`0\ h\leq x\leq 5\ h`

Explanation:

The complete question in the attached figure

Let

x ----> the time in hours

y ----> the distance in miles

In this problem we have a proportional relationship between the variables x and y

The linear equation is of the form

`y=kx`

The slope or unit rate is the same that the constant of proportionality k

The constant of proportionality is the speed of the car

so

`k=(45)/(5)=9\ (miles)/(hour)`

substitute

`y=9x`

Convert to function notation

`f(x)=9x`

The domain of the function is the interval ---> [0,5]

`0\ h\leq x\leq 5\ h`

All real numbers greater than or equal to 0 hours and less than or equal to 5 hours