Write a function that models the given situation.

Question

Determine the domain from the situation, graph the function using the domain and identify the range. a bicyclist travels at a consistent speed of 12 miles per hour for 45 minutes.

Answer 1

Hi, Abigail.

 

Okay, so the function is: (distance = rate x time)

t = time

f(t) = 12t

Because t = 45 minutes, then

f(t) = 12mi/hr x 1hr/60min x 45 min

 f(45 min)) = 9 miles

 

The domain is all real numbers ≥  0 because you can't have a negative time.

The range is all real numbers ≥ 0 because you can't have a negative distance.

Answer 2

Let y = the distance traveled; let x = the time traveled in hr:

 

y = 12x

 

So, for example, 9 = 12 x 3/4, x = 3/4, y = 9

 

So, for example, 12 = 12 x 1, x = 1, y = 12

 

So, for example, 24 = 12 x 2, x = 2, y = 24

 

If x = 0, then y = 0

 

Domain = all values for x that make y a real number.  

 

Domain would be all real numbers > 0

 

Can't graph on this site...