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Find the absolute maximum and minimum values of each function on the given interval. Then graph the function. Identify the points on the graph where the absolute extrema occur, and include their coordinates. $$f(t)=|t-5|, \quad 4 \leq t \leq 7$$

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So the question is asking about the money, people, things about Ed. Graphs of given garage is like this. So this is why exes. This is our acceptance or really laugh or net? I have not. Right. So this this Alexis And this is our X axis. No, the graph is like this. This point is minus four, and this point is minus toe. So from here, we will stop, and it will go till minus two. This is my ass too. So from here to here, then we will connect it with or isn't now this point? And then this is one only. And this is minus one only. So from here, it will go to this. This is the equation. No, we need to find out the domain or function. So what we can put in this equation. So here you can put anything from minus four toe the plus infinity because we have the values from minus four from minus four to plus infinity. So we will know that we have a draft only for minus four to infinity. So that's why this is the moment now the range or function up. So you are getting the values for this. You are getting the values for dysfunction from my nest one or you can say from zero to minus infinity or you can say from minus infinity to zero. This is the range because we are not going in the Pacific side off the Y axis of this is the rent. And then the hard part is asking about the indulge where dysfunction is constant, constant. It means the value is not getting tensed. So from the minus four minus toe, the value is same, which is minus two only so minus four minus toe the crunchiness on stent. Now the four part of the kitchen is asking in the world where function is decreasing. So from here, this will you will, you can say in the accident if you want to know that from zero to plus infinity, the function is decreasing. And then where the question is asking that interval where the function is increasing, one function is increasing from minus two No. Zero. So this is the increasing part, and then the question is asking the number activate function APP has a related maximum and the little maximum or function. So the value where it have a little maximum. This is the maximum value which dysfunction can have, which is zero and where it will have it will have on exit was 20 So it actually goes to little. Why really will be a little which is maximum. So this is the answer for Interval? No, The question is asking that What is the value for F minus three plus Oh three. So this is minus two. So this is minus two and this is minus three. So f minus three will have a value is minus to plus after three. So this is the aggression way have Why is it was toe minus six. This is no active Zika as to what? This is a quest to actually close to minus y. So we will help. When is it close to three. Then I really will be minus three. So my mystery so minus to plus minus three, which is minus five. So this is the answer for F three plus f minus tree. No, the Russian is completed Over here. We have been the analysis off this graph and this is the complete answer of this Russian

The next question we're going to function effort teams to go to two mice Absolute value t who, like the one is less or equal t which is less wrinkles at three and we're first were asked to find the absolute extreme values are accident. Move, Max More minimum the star athlete three Friend of primary t surgery operative to my eyes Absolute value of tea which will get us t over after value Tea The tea over absolute reality with zero won t is equal to zero. So that is our critical number so different outside Maximilien We caves are side points in our critical values that we have from a one to minus off the bottom end of one which is equal to one we have off of zero which is equal to to my eyes off the knowledge er which should be put to we offer three. Would you take the tune less up the value of three, which is just equal to negative one. So we're left with the absolute minimum. Maybe want absolute maximum to it's a Mexican draft. This so we haven't spittoon myself ups. If I were you Excellency, maybe 123 can see you want to. Three One source Unequal to Thanks. What does us no equals? Three? It still gets your absolute maximum is That's just too. Now someone is all I've done here. Out. One are at 91. So this is our answer.

So for this problem we are given a graph and we were asked to determine determine each of the following things listed below. So for a we're going to start with the domain which would be from negative 3-5 in brackets. Yeah. Um even though there's a hole here, it does go here at three and then pick right back up after. So that's why I would be in brackets. Um he is going to be how low and high it goes to the range, so that will be from negative 2-4 also in brackets. Um see once the x intercepts, so it crosses here at -1, 2 and five. Do you want the y intercept? Which would just be why equals negative two. E wants the intervals of increase so that it looks like it's increasing from here to here. That looks like the only interval. So that would be from zero on the X 23 and then decrease would be from here to here. So that would be from negative 3 to 0 and then also from 3 to 5 it's decreasing. Um Gee says the number at which F has a maximum value. So that would be right here, that would be negative three and h wants the actual maximum value which would be the height here which is for and then finally I want F. Of three. So you will go to three on this graph and figure out what is the y value. That's gonna be too, it's not going to be three because there's an open circle there. So you want to look for where there's a closed circle, so F. Of three would be too. Mhm.