Let's observe the given .
f(x)=⎩⎪⎪⎪⎪⎨⎪⎪⎪⎪⎧-2,-1,0,1,if -6≤x<-5if -5≤x<-3if -3≤x<-2if -2≤x<0
Graphing the Function
To think about how to draw the graph, let's look at the first piece of the function. The restriction on the tells us that
f(x) equals
-2 when
x is
greater than or equal to -6 and
less than -5.
f(x)=-2 if -6≤x<-5
To graph this, we draw a at
y=-2 extending from
x=-6 to
x=-5. To indicate that
x=-6 is contained in the , we place a closed circle at that point.
x=-5 is not contained in the solution set of this piece, which we indicate with an open circle.
Following a similar process, we can graph the other pieces of the function.
Domain and Range
Now that we have graphed the function, we can describe its domain and .
Domain
The domain of a function is the set of
x-values for which the function is defined. From the graph (and the function rule), we can see that
x can equal any value from
-6 to
0, not including
0.
-6≤x<0
Range
The range of a function is the set of
y-values for which the function is defined. From the graph (and the function rule), we can see that
y can
only equal
-2,-1,0, and
1.
{-2,-1,0,1}