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For the piecewise function, find the values h( - 9), h(O) h(2), and h(9). Sx - 14, for X < -4 h(x) = 2, for - 4sx<2 X+8, for x22h( - 9) = [h(o) =h(2) =h(9) =...

Question

For the piecewise function, find the values h( - 9), h(O) h(2), and h(9). Sx - 14, for X < -4 h(x) = 2, for - 4sx<2 X+8, for x22h( - 9) = [h(o) =h(2) =h(9) =

For the piecewise function, find the values h( - 9), h(O) h(2), and h(9). Sx - 14, for X < -4 h(x) = 2, for - 4sx<2 X+8, for x22 h( - 9) = [ h(o) = h(2) = h(9) =



Answers

For each piecewise function, find the specified function values. $$\begin{aligned} &h(x)=\left\{\begin{array}{ll} -3 x-18, & \text { for } x<-5 \\ 1, & \text { for }-5 \leq x<1 \\ x+2, & \text { for } x \geq 1 \end{array}\right.\\ &h(-6), h(0), h(1), \text { and } h(4) \end{aligned}$$

So we have this function G. Fx and it's a piecewise function. We're just gonna look at a different couple values of this function. Um And it's going to be equal to one of these three equations at that X value based on these um conditions here. So if X is less than negative five, we used the first equation of exes between negative five and if it's actually greater than or equal to negative five but it has to be less than one, then we use the second equation. And and if X is greater than or equal to one, we use the third equation. So the first value of X we're looking at is G. of negative five and negative five is not less than negative five. Um So we can't use the first equation but it is less than or equal or greater than or equal to negative five in less than one. Um When X is equal to negative five, this inequality holds so we use the second equation and the second equation is just equal to one. So G. Of negative five is equal to one. The second value we're gonna be looking at is G. Of zero. So if we plug in zero in for X into the into these inequalities which one holds zero is not less than negative 50 is greater than negative five in less than one though. So we're going to use this second equation again which is just equal to one, so G. Of zero is equal to one. Yeah. Next we're gonna be looking at G. Of one so one is not less than negative five. One is greater than negative is greater than or equal to negative five but it's not less than one and one is greater than or equal to one. So we use this third equation which is just X plus two. We plug in one for X one plus two, Which is equal to three. And then lastly, we're gonna look at G. F four. So again, if we go through these any um inequalities here, which one holds, we can see that four is greater than one, it's greater than or equal to one, and that's going to be the only inequality that holds here. So we're gonna use X plus two. Again, plug in four, X four plus two, Which is equal to six. So these are the different The four different G of X values at the X values that we're looking at.

This is sort of a fun problem because. Uh huh. It's basically the you're going to use the top equation for almost everything. You have X squared nine. It's 9 over X plus three. Sorry text -3. Okay. And we use that anytime R. X. Value is not equal to three. And a lot of times we do that because if we were to plug in three into the problem you'd be divided by zero. So you don't want that. So you come up with a piece wise that you define the value Win X equals three. Um So you only use this bottom equation Why equal six win X equals three. Other than that you use the top equation that Y equals that top equation for any other number. So I'm actually gonna jump to let her see Where they ask you to evaluate each of three. And uh yeah you're gonna get an answer of six because that's the only time you use this bottom equation other than that for letter A. We're going to use the top equation for H. Five. I think you can do this math in your head and if you can't, five squared is 25 -9 is 16 And 5 -3 is two. and then divide 16 divided by two. Is we need and then let her be see if I can squeeze it right here is ask you to evaluate each of zero. That's pretty easy because zero to any power in zero. You just left a -9 divided by -3. And the negative out. I named this positive three. So the answers are 8, 3 and six.

Hey, guys, welcome back this problem or asked, observe this piece wise function and then finds from different album values with some given input values. So the first input value we are given is negative. Three. Yes, we will evaluate h of native three and that will fall under a top condition where X is less than zero. That would be too Hamas minus three plus three. We minus six plus three B minus three. The next value any defined is H of minus three halves minus 1.5 that will again be less than zero. So fall under our top condition to times minus three halves plus three, which will be minus three plus three or zero. The next only to find is H of minus 0.1 That is just lightly lessons Europe that will again fall under our top condition two times. Point does your own. It's your of one plus three 002 plus three. It will be 2.9 nine. The next meal you have is a church of one. I never fall under our middle condition on X is between zero and two, so we'll have one squared plus one, she'll be one plus one, actually two. Then we'll have age of two and we look at our conditions here. The middle condition goes up to two but does not include two in the bottom Condition is greater than two but also does not include two. So we actually cannot figure this one out. It is undefined. It has no answer because there is no value for one X is equal to two. And then finally look at h of three. And that will be under our bottom condition when X is greater than two. And our answer is simply five. There you have it. Thanks for watching.

Hey guys, welcome back. So this problem or asked to observe the piece wise function and then find some H values with some given X values. So the first value we need to find four is h of negative five. We can see that negative five is very small, even smaller than negative too. This will fall under a copy of condition for H of X is simply native to h made. A five is negative two, then rest defying What h of negative two is ex's name too. This falls under a middle condition when X is between, including negative two and then up to but not including positive three. And that is simply the absolute value of X. To be the absolute value native to me too, that has to find a church negative 1/2. This is still under that middle condition to be the absolute value of X absolute value negative 1/2 What happened Interested final h of zero is that again falls under that middle condition where X is between negative too up until but not including three again. The absolute value of X just just the absolute value of zero zero interes to find what h 2.999 ISS, And this is just on the very edge of that middle equation. Still, because 2.999 is just smaller than three, so still to see absolute value, Becks. It's the absolute value of 2.999 which is 2.999 and then finally were as to find. But H three is, and that falls under to our bottom equation, where X is greater to or equal than three. In this case, it is equal to three that equation simply five. And there are your answers. Thanks for watching.


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