Suppose you park your car at a trailhead in a national park and begin a 2-hr hike to a lake at 7 A.M​​. on a Friday morning. On Sunday morning, you leave the lake at 7 A.M. and start the 2-hr hike back to your car. Assume the lake is 3 mi from your car. Let f(t) be your distance from the car t hours after 7 a.m. on Friday morning, and let g(t) be your distance from the car t hours after 7 a.m. on Sunday morning.

a. Evaluate f(0), f(2), g(0), and g(2).

Video transcript

Hi, everyone. Let's take a look at this practice problem. This problem says a cyclist leaves their home at 8:00 a.m. on Saturday to ride to a friend's house 4 miles away. The ride takes 1 hour. On Monday, they leave the friend's house at 8 a.m. and ride back home, also taking 1 hour. Let HFT be the cyclist's distance from home, 2 hours after 8 a.m. on Saturday, and let IFT be their distance from home 2 hours after 8 a.m. on Monday. What are the values of H 0, H of 1, I have 0, and I of 1? We give 4 possible choices as our answers. For choice A, we have H of 0 is equal to 0, H of 1 is equal to 4. I of 0 is equal to 4 and 1 of 1 is equal to 0. For choice B, we have H 0 is equal to 0, H1 is equal to 4, I of 0 is equal to 0, and I have 1 is equal to 4. For choice C, we have H0 is equal to 4, H1 is equal to 0, I of 0 is equal to 4, and I of 1 is equal to 0. And for choice D we have H 0 is equal to 4, H1 is equal to 0, I have 0 is equal to 0, and I of 1 is equal to 4. So we're asked to use the information in this problem to find the values of H of T and IFT when T is equal to 0 and T is equal to 1 for each function. So we're going to start off by looking at a function H of T. and the first value that we need to find is H of 0. So HFT represents the distance from the cyclist's home 2 hours after 8:00 a.m. on Saturday. Now we're told in the problem that the cyclists leaves their home. At 8 a.m. on Saturday. So, at 8:00 a.m. on Saturday, they are at their home. That means that they are a distance of 0 away from their home. So that means H of 0 is equal to 0. H of one is the next value that we need to find, and so that it's gonna be one hour after they have left their home. And we're told that they take a ride that is one hour long. And they reach a friend's house that is 4 miles away. So, the distance that they are away from their home is going to be 4 miles after 1 hour. So age of 1 is going to be equal to 4. So now we have our two values for our function HFT. Now let's look at our function IFT. And so here we'll be looking at I of 0, as our first value that we need to find, and I here represents the distance from the cyclist's home, 2 hours after 8:00 a.m. on Monday. Now we're told that. The cyclist leaves their friend's home at 8:00 a.m. on Monday, and their friend's home is 4 miles away. So that means that they are 4 miles away from their own home. So that means that I have 0 is equal to 4, since it is 4 miles away from their home. The next value that we need to find is I of one. So this is going to be after one hour of cycling on Monday. And we're told that they go back home after taking one hour. So, after 1 hour, they're located back at their home, so they are a distance 0 away from their home. So that means that I have 1 is going to be equal to 0. So these are the 4 values that I needed to find. For this question So now that I've found those values, I can look at my answer choices, and the correct answer choice corresponds to answer choice A. So I hope that this explanation has been useful, and I'll see you in the next video.