WEBVTT
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all right, we have this piece voice function,
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and we're going to find some function values and then
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sketch the graph. So let's find f of negative
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three. So negative three falls into this piece of
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the domain. X is less than or equal the
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one. And so the Y value is always going
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to be negative one for that Now let's find F
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of zero zero also falls into this piece. X
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is less than or equal to one, so F
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zero is also going to be negative one. Now
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let's find out of two two falls into this category
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here. X is greater than one, so we're
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going to substitute to into seven minus two X,
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and we get seven minus two times two, and
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that will be three. OK, now it's time
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to figure out how to sketch this graph, and
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so, at least at this point, we have
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three points on the graph, so that's a good
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start. It would also be a good idea to
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think about what each piece should look like. So
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if you think about the top peace, it should
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look like the line y equals negative one. So
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that's just a horizontal line, and if you think
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about the bottom piece, it should look like a
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line with a slope of negative two and a Y
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intercept of seven. Now each line is going to
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stop at some point because we only have a piece
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of each money and the line stop at one.
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So for the first piece, I'm going to substitute
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one in and see what I get when I substitute
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one in. I get negative one. We get
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negative one for everything there, so we know that
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peace is going to stop at the 0.1 negative one
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. So I'm going to plot that point, and
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we know that that peace is also going to go
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through the point. Negative three negative one that we
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found earlier and zero negative one that we found earlier
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so we could plot those points. Negative. Three
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. Negative 10 Negative one. So here we have
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that piece, that horizontal line. The other piece
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is also going to stop at X equals one.
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It's not going to go through one, so we're
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just going to have an open circle at one,
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and the open circle will be at one seven,
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minus two times one. So that would be one
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comma, five open circle there and then we know
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it's also going to go through the point to three
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since we found that point earlier. So we have
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an open circle at the 0.15 It's a little lock
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. My screen. I'm gonna have to just fudge
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it there, and then we have the 0.23 So
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we're going to get a line that looks like this
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for the other piece.