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Graph interpretation word problem: temperature

When a function models a real-world context, we can learn a lot about the content from the function's graph. In this video, we consider a graph that models temperature over time.

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Video transcript

Let T of [t], denote the temperature capital T in New York City measured in Celsius degrees Or degrees Celsius when it's t, lowercase t, hours after midnight on a given day. The function is graphed below The following table contains true statements. Match each statement with the feature on the graph that most closely corresponds to it So once again this is capital t as a function of lowercase t's temperature as a function of time So we see at time equals 0 the temperature is negative 3 degrees Celsius. And then as we go to 8 hours later, the temperature is at Zero degrees Celsius and then it hits a, it hits at least a relative maximum point or at least from what we see it could even be a Global Maximum point but based on what we see, it's definitely a relative maximum point 14 hours into this measurement at time equals 14 and then the temperature starts to go down again. So let's see, so in other words it is t hours after midnight, so this is this is at midnight This is going to be at 8:00 a.m.. This is going to be at noon and this is going to be at 2:00 p.m. And so on and so forth, but anyway. The feature, Y-intercept. So the y-intercept is right over here And we see when lowercase t when time is zero, zero hours after midnight the temperature in New York City is Negative 3 degrees Celsius So it was negative 3 degrees Celsius, at the beginning of the day Yeah, that's a true statement and especially if you consider the beginning of the day, the true beginning of the day is right at midnight so That's that one. The y-intercept tells us this true statement So positive or negative interval and these questions are a little bit tricky because you don't have to use It's the positive or the negative interval It doesn't have to be both, so if either the positive or negative interval helps you with one of these other two statements So let's see. It was getting warmer between 2:00 a.m.. and 2:00 p.m.. The temperature was above zero between 8 a.m.. and 8 p.m. So let's see. If we're talking about positive or negative intervals, so we're not talking about increasing or decreasing We're talking about positive or negative intervals, so we have a negative interval Sorry, we have a negative interval from time equals zero to time equals eight What do I mean by negative interval is the temperature is negative. It goes, it's below zero And then from, time, from eight hours from 8 a.m. To what is this this would be noon, this would be 8 p.m.. From 8 a.m.. to 8 p.m. Or the 20th hour if you're taking in military time, so to speak. We see that our temperature is positive and then it dips down to negative again. So a positive or negative interval tells us when our temperature was above or below zero. And we can see we have this positive interval where the temperature was above zero between 8 a.m.. and 8 p.m. So we're only using the positive interval this interval right over here where the function is positive? That means that the temperature was above zero degrees Celsius between 8 a.m.. and 8 p.m. So once again we don't- It's saying either the positive or the negative interval helped us make the statement. In this case it was only the positive interval helped us make this statement, and then finally we have increasing or decreasing interval. And it was getting warmer between 2 a.m.. and 2 p.m.. It was getting warmer between 2 a.m. Which is right over here. So we see that the function is increasing as t increases so does the temperature, all the way to 2 p.m. And that, right of there, is an increasing interval. So once again we're not using an increasing and a decreasing interval, we're just using the increasing interval, the decreasing interval isn't helping us to make the statement, but the increasing interval is helping us. It's letting us make the statement. It was getting warmer between 2:00 a.m.. And 2:00 p.m. From here to here or between 2:00 a.m.. and 2:00 p.m. We see that the function itself is increasing that is an increasing Increasing interval and we got it, right