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Analyze the graph of the given function Determine fas follows: the end behavior: find the power function Find the- ~intercepts that the graph _ resemblcat the graph...

Question

Analyze the graph of the given function Determine fas follows: the end behavior: find the power function Find the- ~intercepts that the graph _ resemblcat the graph_ Large Fa Determine whether graph crosses toucnes Graph using= the x-axis each x-intercept, graphing utility. Use graph deterine the Ioca Maxima and local decimal places. minima ant eta Romnd tuming paints Use the information obtained in (W) _ dEn complete points. graph of f by hand, Label all inlercepls and turni (9) Find the domain

Analyze the graph of the given function Determine fas follows: the end behavior: find the power function Find the- ~intercepts that the graph _ resemblcat the graph_ Large Fa Determine whether graph crosses toucnes Graph using= the x-axis each x-intercept, graphing utility. Use graph deterine the Ioca Maxima and local decimal places. minima ant eta Romnd tuming paints Use the information obtained in (W) _ dEn complete points. graph of f by hand, Label all inlercepls and turni (9) Find the domain of f Use the graph to find the range of f (h) Use the graph determine where f is increasing 4nd where f is decreasing xox + 2)



Answers

Use the graph of $f$ to determine each of the following. Where applicable, use interval notation. a. the domain of $f$ b. the range of $f$ c. the $x$ -intercepts d. the $y$ -intercept e. interval(s) where $f$ is increasing f. interval(s) where $f$ is decreasing g. interval(s) where $f$ is constant h. $f(4)$ I. the number at which $f$ has a minimum I. the minimum value of $f$

So in this problem we are given a graph and we are asked to list each of these things about this function. So first I want to solicit domain which is going to be from negative four to infinity since this is going on forever. So negative for in a bracket because we're including that point to positive infinity. It's a bracket right there. Now for being the range of this function will be from negative infinity since it's going down forever. Up to positive three and three will also have a bracket since that is a close circle of three. See wants us to list the X intercept, I'm gonna go ahead and move over here. So X intercepts here, we have right here and here. So X equals negative for in positive for d wants the Y intercept which would be at two. E wants the intervals where this function is increasing. So it's increasing from negative for two, negative two. And then it's also increasing. Looks like that's it actually going down here. Yeah, that would be it decreasing and decreasing from negative to to infinity. It looks like, I remember you just list the X values are intervals, jesus, the number at which F had a relative max. That would be right here um negative too. H wants the actual relative max. So that would be when y is three and then I want f of negative three. So what you do here is you find negative three. And the exes And then determine where does it cross the function at -3, 2. So an F is -3. Your y value is too.

According to given diagram, we have to find the domain first. So first began I No man is This is from minus three toe Leslie so minus three Who plus five is doing? No. The range we can itis ranges from minus two to maximum values. Plus for so minus to plus four is the range Hey, this part And despite no no exit does it. So where the graph is cutting Xing just xx is that it's industry. The X intercept is ex acquittal minus one. Who and play These are X and doesn't. Then next is lying, does it? So we can write for way interested. Why is he called O minus two? No, next is in double where f is increasing. It'll f is in greasy everything Reason from and value off Actually a great zero to three from judo 23 effort increasing and f is decrees e well, they say f is big greasy from minus two Beautiful union Tony do fight It is decreasing. Next the number of its f has maximum value s has maximum value But this we can answer that finger graph so effort has maximum value it x equal minus three and the maximum value ALS. Yes, this again they ask maximum value off if this is bless food at this point at maximum value till every agency this is for next is after the we have to find so at X equal to three the value off F at X, equal to three. We have to consider this point because this is closed. This is plus two. So this is a little less too.

They want us to steady The function of X is equal to you before my ass x to the C that power Well, for my graph, it appears that leader man is from zero you and unity. So zero affinity they range well, that's good as a maximum for and it's decreasing forever. So the range will be or downward Thio. Well, we can plug in his big numbers You want into that become negative and correct before. So this should be from negative infinity. Although it up to you for okay, No, the term in the intervals for which it is increasing and decreasing What we know that is decreasing, um, on its entire domain. So from zero to infinity does not appear to be increasing anywhere Yeah.

I started doing number 42 and we have the structure that we want a graph. I have four minus X to the power of 2/3. So we have something like this. And if we want to figure out the dough made, we just look at all the possible exercise because, you know, we could put the next values for both the Russians. So our domains from they're gonna infinity to infinity and for a range, we could see that we could go all the way here today. Your affinity, the highest wife you could get is right here at four. So our ranges from their gun affinity to four to see where we're increasing. Well, we can see that That's the left part of this graph from there. An affinity for and to figure of. Over decreasing. Well, we could see that That's the right section of this crap. So that this room zero to infinity


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