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Graph interpretation word problem: temperature

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 core 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 Maxima but but based on what we see it's definitely a relative maximum point 14 hours into into this measurement at time equals 14 and then the temperature starts to go down again so let's see so advertises 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 0 0 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 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 time equals eight what do I mean by negative interval is the temperature is negative it goes it's 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 go 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 with 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 and decreasing it but we're just using the increasing interval the decreasing interval isn't helping us to make the statement but the increasing interval is I'm helping us 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