Air force one can travel 630 miles per hour. Let h be the number of hours traveled. the function d=630h gives the distance d in miles that air force one travels in h hours. A. Identify the independent and dependent variables. Write d=630h in function notation. B. What are reasonable values for the domain and the range in the situation described? C. How far can Air Force One travel in 12 hours?

Respuesta :

The independent variable is the input in the function.
Usually, when you have a function written as y in terms of x, x is the input and the independent variable. Here you have d in terms of h. You can calculate the distance if you are given the hours, so hours, h, is the independent variable. You can use any number you want for h. Once you input h into the function, then d, the distance, depends on h, so d is the dependent variable.

d = 630 h
h is the independent variable.
d is the dependent variable.

Function notation uses the name of the function, and the independent variable inside parentheses.
Since this function is solved for d, and it it a function of h, you'd use d(h)

d(h) = 630h

I'm not sure how long an airplane can travel without stopping for fuel, but let's guess it's under 24 hours.

The domain is the values the independent variable can have.
My guess is the domain is from 0 to 24.
We now calculate d(24)
d(h) = 630h
d(24) = 630 * 24 = 15.120

In 24 hours, the airplane travels 15,120 miles, so the range is from 0 to 15,120 miles.

In 12 hours, the airplane travels

d(h) = 630h

d(12) = 630 * 12

d(12) = 7,560

In 12 hours, it travels 7,560 miles.