WEBVTT
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here we have a piece voice function, and we
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want to find some function values and then sketch the
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graph. So let's find f of negative three.
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So negative three falls in this piece where X is
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less than two. So we're going to substitute negative
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three into three minus 1/2 X. We get three
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minus 1/2 times negative three, and that's going to
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be three plus three halves. So that's nine house
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okay f of zero for F of zero. We're
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going to plug zero into this piece as well,
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because zero is in the interval. That's less than
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two. So we have three minus one halftime zero
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, and that's going to be three. And then
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for F of two, we're going to substitute to
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into the bottom piece since two Falls and the X
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is greater than or equal to two category. So
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we have two times two minus five, and that's
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going to be negative one. Okay, so we
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have those function values and those will help us when
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it comes to graphing. But here's how I like
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to graph a piece Wise function. I like to
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start by thinking about what I'm expecting to see.
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So for the top piece, I'm expecting to see
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a line that has a slope of negative 1/2 and
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a Y intercept of three, but only part of
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that line. And then, for the bottom piece
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, I'm expecting to see a line with a slope
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of two and a wide receptive negative five Onley part
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of that line. Both lines are going to end
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at X equals two. So for the top piece
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I'm going to plug into now. I can't technically
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plug into because two is not in that domain.
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But I can make an open circle there. So
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if I substitute to and there I get three minus
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1/2 times to, and that's going to be,
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too. We're gonna have an open circle at 22
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And then if I substitute something less than two in
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there, Well, I've already got one negative 39
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house so we can plot that point. So we
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started our open circle at 22 We go through negative
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39 halves. It's up here somewhere, and we
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keep going, so that should look more or less
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like a line with a slope of negative 1/2 and
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a y intercept of three. I could probably make
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it a little bit more accurate. So let's find
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Ah, height of nine house. That would be
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34 way up there a little bit higher. Okay
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, now for the other piece. So it starts
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at X equals two. We already know the point
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to negative one from the work we did earlier and
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let's find a second point. So another point that
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is greater than two. We could use three,
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for example, so two times three minus five would
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be one. So now we start with a closed
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circle at the point to negative one, and we
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go through the 0.31 and keep going. So does
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it look like we ended up with the line with
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a slope of negative 1/2 in a Y intercept of
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three? That would be that one. And does
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it look like we ended up with the line with
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the Y intercept of negative five and a slope of
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to You can imagine that when continuing down further and
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that seems reasonable