Exploring key features of functions

0:00- [Instructor] We are told four friends volunteer at an animal shelter. The graph shows the number of dog treats in scoops as a function of time in minutes for one of their treat packing shifts. So let's see, as time goes on in minutes, the number of treats packed in scoops.

0:19So let's see, they're at 0, then after a while, let's see, it looks like about 25 minutes they get all the way to 10 treats packed, 10 scoops of treats. And then it looks like they're not packing much for the next, looks like 15 minutes, but then they start packing actually at a faster rate.

0:34And then they stop packing for a little bit and then they pack at looks like a slower rate than even, or actually maybe a similar, actually no, a slower rate than they were doing even in the beginning. All right, match the graph with the treat packing description that could represent it.

0:46Pause this video, have a go at that before we do this together. Okay, let's just read them one by one, and only one of these is going to be the choice. Malin starts by packing treats quickly for 10 minutes. She pauses to chat for a few minutes, then packs treats more slowly.

1:03She takes a longer break and then stops for the rest of her shift. So, the graph shows the number of dog treats for one of their treat packing shifts. Okay, so this isn't their combined, so maybe this is Malin. Let's see if this makes sense. Quickly for 10 minutes, she pauses to chat for a few minutes.

1:23Okay, quickly for 10 minutes would probably look something like this. Probably packing quickly for 10 minutes and then pauses. And then pauses for a few minutes. They don't say what it is, but it would be some type of a pause and we don't know how quickly it is.

1:38Even if this is considered quickly, there would be some type of a pause right over here at 10 minutes, which we don't see. So, I am going to rule this one out. Nico begins with a steady pace, speeds up a little, and then keeps speeding up the entire time without stopping.

1:52No, that's not a description of here because whoever's doing it is stopping. They're stopping twice. Padma starts with no treats packed, but then unpacks some treats to redo the bags. She takes a break and then keeps moving for 25 minutes. Then, she takes another break and continues unpacking again.

2:12See, Padma starts with no treats packed. All right. But then unpacks some treats to redo the bags. I don't know what that means, to redo the bags, but then unpack some treats to redo the bags. If she's unpacking some treats to redo the bags, I would, she's unpacking things, not packing, so maybe it would go negative initially.

2:40So, I don't think this one is right. So I'm gonna remove this one. Let's hope that D is right. Dermot, I guess is how I'd pronounce their name, Dermot begins packing treats at a steady pace, stops to refill the bins, then packs treats much faster for a while. He stops again to label packages, then finishes by packing at a slower, steady space until he reaches a total of 40 scoops.

3:05Yeah, this looks pretty good. Packing at a steady pace, that's that right over there. Stops to refill the bins, so, refilling the bins right over there. Then packs treats much faster for a while. That is this over here. He stops again to label bags, so this is when he is labeling the bags.

3:26And then finishes by packing at a slower, steady pace until he reaches a total of 40 scoops. And we already said this is a slower, steady pace and finishes at exactly 40 scoops. So, I like choice D. And we're done.