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Use linear interpolation (see example 3.8 ) to estimate $f^{-1}(b) .$ Use the apparent curving of the graph to conjecture whether the estimate is too high or too low. $$(1,12),(2,10),(3,6),(4,0), b=8$$

So here we see that the points the point, Q one, which is one over AIDS. One over 41 over. AIDS. One of its ooh is inside the convicts. All off s. This is because the bar's century coordinates bar century coordinates are all positive. Andi Also, some of the one no points Cute, too, Which is three over four minus one of the 401 of a two on um que full, which is zero minus 203 They're outside the convicts all off his because they contain negative Seve Barris entry coordinates. Gin. It's unless they got some Q five. We see that the points Q five, which he called to won over 31 over 31 over three comma zero is on the face containing the foetus ese V one v tsu victory. Because the forced three coordinates are positive on some of the one on the force co ordinate zero. So what? We have left his q three. So we have a queue theory which is giving us zero theory of a 41 over 40 is on the line. Segments off. Vite sue victory. This is because the second on Dhe toward Ward needs our posits, ese. On some soo wan on the forced on fourth Ward needs zero, uh zero. We can say this is the hottest. Sees Vince who on?

Received at the points. The points Q won't, which is given us one over AIDS one over 41 over ends. What over it soon is inside the convicts, all of theirs. This is because, but Barry centric Orjan needs all positive. He's Andi. Also something warm? No, the points cute Sue on cue. For Which is it? Walter? Were cute. Suit is three over four minus one of the 401 of a zoo and then Q for zero minus 20 comma three. They are outside the convicts all off earth because be Considine Negative Bar Centrale coordinates. Ordinates. No, the points Q three, which is given a zero the year before. One of our 40 is on the edge. Do swing Vergis ese v tsu on victory. This is because this second on towards it's second on toward coordinates our course. It's Eve. I'm something Warren on the forced on fourth co ordinates zero. Now, lastly, we have Q five is on the fins. Consuming the bodice is V one v. Tsu on victory. This is because the forced 3/4 needs war grenades. Uh, faucets on something. Warren, we're us. The fourth coordinates zero is zero

Okay, So for this particular problem were asked to use, um, kind of graft this and determine the interpolation toe estimate, the inverse of the value. So our first point is gonna be 1 12. Our next point is to six and then 32 and then 40 So it looks like it's going to curve kind of like this and then were asked to estimate the or B is five. So if we have an inverse where why is the input X is the output and were asked to find the input that is five. So we look on our graph and we find out where it's five, so it's somewhere right around here, and so I would estimate this to be about 2.1 or 2.2 somewhere in there.

Okay, So for this problem, we're asked to use linear interpolation. Eso were given the points, um 1 12. So I'm gonna go ahead and plot these first. So I have my y axis going in terms of twos. So? So I'm gonna have 1 12 here, and then the next point is to 20 and then 3 26 and then 4 30. And so we have a curve. That kind of looks like this. And so we're asked to estimate what 23 would look like. So So 23 is going to be somewhere right around here. So based on the location of the graph, I would say that the inverse of 23 So keep in mind that in verses have r y value equals the X value. So if my wife value equals 23 then my ex value is gonna be somewhere around 2.5