Hi.
What I'd like to show you is how to graph a piecewise function.
Given this function I'm given kind of three expressions.
And I'm given three constraints.
So all that a piecewise function is,
is really kind of three different now lines
that we have to graph.
And now they have constraints on them.
Because usually when graph linear lines,
they go from negativity infinity to infinity for both
your domain and your range.
But now what we've done with the piecewise functions
is we've make constraints on our lines.
So what I'm going to first do is I'm
going to rewrite each one of these expressions in a y equals
mx plus b form.
So then I can just kind of get my mind set up
with what they actually mean.
So this expression would be y equals a negative 1.
This would be y equals 2x.
And this would be read as y equals 6.
So now I'm starting to think of these.
I need to say, all right, well if I remember
my y equals mx plus b form, I need
to say, all right, what is going to be
the y-intercept for each one of these equations.
And then what is going to be the slope?
If I look at this first one, I notice that there is no x.
So therefore I have no slope.
And my y-intercept has got to give me a negative 1.
Therefore, This is going to be a constant line at negative 1.
Now when graphing a linear equation,
I notice that I have constraints.
This graph is only true when x is less than or equal to 0.
So what I can do, there's a couple of ways you could do it.
You can just graph it as when it's only true.
Or you can maybe just graph the whole equation
and then start erasing where it's not true.
And I'm going to go through that just
so you guys can kind of see what the whole graph will look like.
So x equals negative 2.
Actually Samantha, do you see that red marker right
on the folders?
In My Folders, in my folders to the right,
you'll see a red marker.
Yep.
Can you throw it?
Well, underhand toss it.
You know you're making a video, right?
I know.
OK, so if I was going to graph this at negative 1,
I'd go down to negative 1.
All right, now I say all right, it's
only true though when x is less than or equal to 0.
Well, where is 0?
Where x is 0 is right at the y-intercept.
So therefore this graph, I'm only going to shade
in where it's true.
We're not going to draw where it's false.
We don't care about where it's false.
We only care about where this equation is true.
So it's only true when x is less than or equal to.
Since it's equal to, it's going to be a closed circle.
Next point, y equals 2x.
What does that graph look like?
Well, I know that my slope now has a slope of 2 over 1.
And I do not have a y-intercept.
I'm sorry my y-intercept is 0, since it's not
labeled up there.
So I do have a y-intercept.
It's 0.
But it's not shown in the equation.
So therefore, I know it's 0.
So therefore on this to graph it,
if my slope is now 2 over 1, that
means I'm going to rise 2 go over 1, rise 2 over 1.
So now we're down 2 to the left 1,
and down 2 left 1, and then down 2 left 1.
So again, I'm just going to dotted line,
just so I approximately know what
my graph is going to look like.
Then it says this, however, this graph
is only true from 0, when 0 is less than x or less than
or equal to 3.
So therefore, since it's just x is greater than,
it's going to be an open circle.
And it's going to be between 0 and 3.
So I'm going to go over 3 1, 2, 3.
And I'm going to follow that up to my graph.
And now this is going to be actually less than
or equal to 3.
So it's going to be a closed dot.
And I'm just going to shade in this graph here.
So that is between 0 and 3 is only
when this equation makes sense.
That's the only time that equation is true.
All these values over here and these values over here,
it's not true under these constraints.
So I'm not going to include them in my graph.
And then lastly, I have y equals 6.
Again, it's just like y equals negative 1.
The y-intercept is at 6.
And it says it's only true when x is greater than 3.
So therefore at 3 again.
I'm right at my 3.
That dot really should be about there.
Sorry guys.
I don't have graph paper on my board.
So I've got to be close to approximate as possible.
x would be at 3.
1, 2, 3.
At x greater than 3, this line, this dot, would look like this.
However, I'm only concerned about when it's
greater than or equal to 3.
So it's roughly going to be right there.
I understand from home you guys can
see that my graph right here is not going
to be the best in the world.
Because I'm just making up my scale.
And it's not exact.
But your graph should roughly look something
into this format.
And now guys, you can see, the blue is all I'm concerned with.
So I'm just going to simply erase away my red.
Because those are points that do not
mean the constraints of my piecewise function.
So there's no point in having them on there.
I just used them as a template to graph
the rest of my equations.
All right?
So that's how you graph a piecewise function
when given your equations and your constraints.