Scenario Type Problems

Question

Answer the following questions based on the  scenario below:

 

Mr. Joyner is at a hotel 240 miles from his home. He is driving at a constant rate of 40 miles per hour towards home.

 

1. What is the independent variable?

 

2. What is the dependent variable?

 

3. The domain?

 

4. The range?

 

5. How would this scenario change if a constant, c, were added to the function?

 

thanks :)

Answer 1

1. Your independent variable is time (in hours). When time is involved, it's almost always the independent variable, since the independent variable is the thing we control. If this were an experiment, you'd be asking, "at 5 hours, how far has he driven?"

 

 

2. Your dependent variable is distance driven (in miles). The distance he has driven depends on the amount of time he's been driving.

 

 

3. The domain is all possible values for your independent variable. For this problem, we're interested in the times Mr. Joyner is traveling, from when he leaves the hotel to when he arrives home. We don't know what he did before or what he's doing after. He leaves the hotel at 0 hours (since that's when he started), and he will arrive home after 6 hours (d = rt --> 240 = 40t --> 6 = t). That means the domain is 0 ≤ x ≤ 6.

 

 

4. The range is all possible values we can get for the dependent variable, based on the values we're allowing for our independent variable. At x = 0, he's driven 0 miles. By the time we get to x = 6, he's driven 240 miles. So, the range is 0 ≤ y ≤ 240.

 

 

5. The function looks like this:

 

y = 40x,

 

since he drives 40 miles for every hour that passes. Adding a constant c gives us:

 

y = 40x + c,

 

which means he's driven 40 miles for every hour that passes, and another c miles on top of that. Basically, it means he started out some number of miles into a trip (c miles), and now we're measuring his distance driven including those miles, which happened before we started the timer.