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6-3 Day 2 Exponential Functions

Added Feb 08, 2019 •

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all right hey guys some. To we finish these two guys can skip to the next problems button. One we did not finished even if we barely gotten started by you guys how to use your calculator so if you haven't done so already please take a second leave something on my desk and then borrow calculator because you will need one today so if you need to pause this right now do that so you guys can grab a calculator so we started this is X this is -2 4 to the X and then we said that we choose numbers negative to negative 1 0 1 2 and so I showed you guys how to plug it in on your calculator and you yesterday we did this and I believe we got one over eight is it going to snow again -1 -2 four to the negative one which is then 1/2 -2 four to the 0 equals made 2 negative skew for to the one equals movie and then -2 * 4 to the 2 okay sober me three tooth too big of a number so I'm not going to grab that one but I will grab the other one and so that it's not a perfect science O negative one ain't that just like a little bit past zero and negative 1/2 that's like halfway -2 0-0 native to I want -8 so to you and that was three struggling Stadium and the negative 8 the 1 2 3 4 5 6 7 8 and so then we're going to connect it with a nice smooth line or as smooth as possible I don't know why my arrows going sideways that song you should look something like that take a second if you haven't already and practice the calculator make sure you guys remember how to get those answers if you don't ask person next to you and if they don't know last person like who do we should get it in like that maybe not as quickly as mine looks but should be nice to move car but next thing we're going to do is describe the domain in the rain will get to the comparing but we're going to do that in a second before the next problems so domain are able to go out for a in both directions so what does that mean means all real numbers for this problem is my graph above the x-axis or below the x-axis it's cool though so that means that Y is less than 0 and can remember there's like a little dotted line here that's it that's our asymptotes that says that it cannot pass here reminds me of life. now I can't remember in Lord of the Rings where he's like you shall not past it's the same this graph could not that Gandalf Gandalf like you will not pass anyways soap for number 6 we're going to head to the same thing so we're unplugging xpa-2 1/4 to the x I'm going to gain what numbers are we going to use if we don't know what where to start negative to negative 1 0 1 2 and so if you and your partner will go ahead and pod this year and neither can meet us in and see what answers you get and then push play and I'll show you my answers good still those are the answers I got you should get 32821 half an 8th of basically the same as the other numbers but they should be I am positive you can go ahead and plot these points so I have an idea 2:32 I'm not going to grab that one cuz it's too big but I'll draft -1 8 1 2 3 4 6 7 8 and then 02 1 Antoine and then we do our best to connect it with a smooth curve oh my goodness that was terrible hold on I'm going to just like that so she can I make a smoothie line and then I can remember that there's an asymptote right here saying that this line cannot pass that asymptote until then our domain here are domain hears all real numbers until then for our range is our graph above below the x-axis this time it's above so now why is greater than zero and basically RSX with his awesome tell which will be in Port make note at in just a second here the benefit for these few problems if you need to pause and finish copying down you can I'm going to go ahead and keep going okay so now we're looking at this problem and this is where. She should be starting as well what do we notice is different about this problem from other problems that we've been working on the Hulk you're saying there's like a -3 here and a plus-2 here hopefully those are the two things that were noticing as different as a plus-2 I'm so that's going to move my so are dotted line that's normally on the x-axis now it's going to move it are awesome chill up chip so I'm going to go ahead and draw it and it's just like a little horizontal dotted line we moved it up to and then this x -3 right here remember any time we had don't write this down anytime we had something like y equals absolute value x + 4 + 2 so the + to an outside moved it up or down so then that's what this is you ain't moving up or down what was really important something that was inside absolute values that you had to make sure that we know of how to switch the sign so you make sure that we switch our sign it's like going to be true always we're going to have to switch to find for x and so far are asked here we're going to do just that we're going to switch I find so now it's going to become three positive 3 and it's going to go and it's going to go in the middle of our chart here so I'm positive he's going to go here and now we're going to pick 2 numbers that go above and two numbers that go below so if I'm going to go 3 I'm going to go backwards to 1 + 345 so now these are the numbers that I'm going to plug in to my graph negative to negative 1 0 1 on this is kind of like our new there's a number up there that becomes your new Middle where is normally zeros the middle and this case now you change the sign here change the time so then we're going to go ahead and plug it in for to the x - 3 a stupid and on your calculators were actually just going to plug it in the exact same way I kind of like I'll show you so when I plug it in 4 - 2 and then this is going to become 1-3 and so I just simplify it just a little bit before I plug into my calculator and make 4 * 2 and then what's 1 - 3 negative to you and you just have to make sure you pay attention to the negative but we do get Negative to you and then update + 2 Thunder calculators are literally going to write the same make sure you put parentheses for this one so I calculator you type 4 parentheses 2 the up Arrow parentheses negative chill and then you can just put plus two and are calculators the one at least that that I'm letting you borrow you can just type it in straight like that and it'll show you the answer so actually that's what I'm going to do right now my calculator you guys should take the back and do it as well at 3 Tim Ervin so that I'm just going to go through in time do the same thing four times to plug in the neck and then 2-3 gear is going to be negative 1 until then I'm going to plug it in for all of these even if the numbers positive you want to make sure that you put your exponent in parentheses that way it doesn't correct that way or calculator knows what to do first so then when I plug it in I get four and then I'm going to keep going and or change to and then here I'm going to get 3 - 3004 * 2 to the 0 Plus equals 4 * 23 months I'm sorry 4 - 3 so then for Masters one bb10 2 minutes going to be 18 cancel now I'm just going to plot these points I have positive 1/3 so right here and then I have positive for this Warren G. 410 and Central going to be the last one I grab anything more than 10 I wouldn't expect you guys to get bra and then 10 I'm so then we going to see Airline is swooping like this and so now our new barrier sorry that that whines all of our new barriers going to be at 2 and so the only thing it really does is just it's at changes are domain and range so now our domain is all real numbers still just because removed that doesn't change our domain but our range now is a y is greater because it's above the asymptote greater than 2 so whatever you're awesome totes that's where your range is going to be at and I think on your paper I put like describe the Transformations so for the Transformations we put in a positive three so we went right three and then we went up to so those are the Transformations I want you to kind of just drive right now and we'll get more in-depth with those later so I'm going to try the next one with you guys and so here I see the negative one so I'm going to start my asymptote down here at -1 Lanham of the X and then this is now your two cousins to the x + 2 - 1 x + 2 again I'm going to put it in the middle and switch the signs and that's naked 2 + -1 + 0 + -3 + -4 and so then I'm just going to plug it in set up out of space so I'm actually asking to add 0 + 2 is 2 and then Denny's going to make sure you put that in parentheses that way it's don't your coupler does it correctly knows what operations to -1 + 2 is 1 -7 New York 2 * 92 + 2 + 0 what's -3 -2 wake me up at 1 can't miss this one turns out to be a fraction answer so I am using my fraction to decimal button so I get -5/3 which is like one point sir 1.7 I'm so just like more than one and then I'd last but not least again 84 + 2 is -2 - 1 which gives me 11/9 which was also I think like two points 1.2 sorry -1.2 and -1.6 year go ahead and grab my points zero 19 too much negative one negative side in 1 2 3 4 5 6 7 but their negative 2/3 and then 1.60 1.6 is like the higher point of one or the lower plan I guess since we're talking about night is this so again it's getting really close but not actually touching can you play some Sublime so there and then here until then for our Transformations all I want you guys to be able to do is identify that we in this case left to and down one and then I domain all real numbers and our range is y why is now it's below so it's going to be less than -1 Pennsylvania can you and your partner go ahead to the next one and the next thing you're going to see for this last one is going to be your answers the only thing I want to find out if there's nothing out of here so try to the ex up here so that means that zero goes in the middle and we're going to use negative to negative 1 0 1 and 2 again but we will shift up your asymptote to 3 all right next thing you'll see the answers to go ahead and bothering here for you okay so here's the answers kids are answers their domains all real numbers range Y is greater than 3 because it's above the line and then we went up three so that's it for your notes for today I will be here after school if you guys need help bye have a great weekend at home or sup on the board

Uploaded by Lauren Stouffer.

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6-3 Day 2 Exponential Functions

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