SOLUTION: Given the following piecewise function: {{{f(x)=system(matrix(3,3, 2x-4, for, x<-3, -1, for, -3<=x<=4, -x, for, x>4))}}} a. Find the domain. b. Find the range. c. Find

Given the following piecewise function:



Let's graph it first.

Get two points for the left part of the graph, which is

y=2x-4, choose x left of the endpoint -3, say -5, (-5,-14)
Now choose x at the endpoint (-3,-10) [but we will stop the line just
before it gets to (-3,10) and draw a circle at (-3,10) because
the graph does not include x=-3 because of the x < -3.

y=-1.  The middle part of the graph is just the line y=-1 which is a 
horizontal line from (-3,-1) to (4,-1).  Put a solid circle at
the endpoints because it includes both endpoints because of the
<'s on both ends. 

y=-x.  Get two points for the right part of the graph. Choose x right of
the endpoint 4, say 6, (6,-6).  Now choose x at the endpoint (4,-4) 
[but we will start the line just after (4,-4) and draw a circle at
(4,-4) because the graph does not include x=4 because of the x > 4.
 
So the graph is:





 a.
 Find the domain.

All values of x can be substituted, so the domain is (,)
 b.
 Find the range.
 
The values of y never go above -1, but they can be -1 or any value below -1,
and since the graph includes points where y=-1, the range is (,-1].



c.
 Find the intercepts.

There are no x-intercepts because the graph does not cross the x-axis.
The y intercept is (0,-1) because the graph crosses the y-axis there.


 d.
 Is f continuous on its domain? If not, state where f is discontinuous.

The graph is discontinuous at x=-3 and at x=4.


 e.
 Graph the function

We already did.

Edwin